Calculus of Variations and Geometric Measure Theory
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GeMeThNES

Authors: L. Ambrosio, G. De Philippis, B. Kirchheim
Title: Regularity of optimal transport maps and partial differential inclusions
Journal: Rend. Lincei - Mat. e Appl.
Year: 2011
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Accepted Paper

Authors: L. Ambrosio, A. Figalli
Title: Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces
Journal: Ann. Fac. Sci. Toulouse Math.
Year: 2010
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, A. Figalli, G. Friesecke, J. Giannoulis, T. Paul
Title: Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data
Journal: Comm. Pure Appl. Math.
Year: 2011
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: A. Mondino, T. Riviere
Title: Immersed Spheres of Finite Total Curvature into Manifolds
Journal: Advances in Calc. Var.
Year: 2011
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, M. Colombo, G. De Philippis, A. Figalli
Title: Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case
Journal: Comm. Partial Differential Equations
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, M. Colombo, S. Di Marino
Title: Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope
Journal: Advanced Studies in Pure Mathematics: "Variational methods for evolving objects"
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, G. Crasta, V. De Cicco, G. De Philippis
Title: A nonautonomous chain rule in $W^{1,1}$ and in $BV$
Journal: Manuscripta Math.
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, A. Figalli, E. Runa
Title: On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces
Journal: Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, N. Gigli, A. Mondino, T. Rajala
Title: Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure
Journal: Transactions of the AMS
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, T. Rajala
Title: Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces
Journal: Ann. Mat. Pura Appl.
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: G. De Philippis, A. Figalli
Title: $W^{2,1}$ regularity for solutions of the Monge-Ampère equation
Journal: Invent. Math.
Year: 2012
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Does this publication acknowledge the ERC funding? yes

Authors: A. Mondino, S. Nardulli
Title: Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions
Journal: Communications in Analysis and Geometry
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: A. Mondino, J. Schygulla
Title: Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds
Journal: Annales IHP-Anal. Non Lin.
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: T. Rajala, K. T. Sturm
Title: Non-branching geodesics and optimal maps in strong $CD(K,\infty)$-spaces
Journal: Calc. Var. Partial Differential Equations
Year: 2012
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Does this publication acknowledge the ERC funding? yes

Authors: G. Citti, M. Manfredini, A. Pinamonti, F. Serra Cassano
Title: Poincaré-type inequality for Lipschitz continuous vector fields
Journal: JMPA
Year: 2013
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: G. De Philippis, A. Figalli
Title: Higher integrability for minimizers of the Mumford-Shah functional
Journal: Arch. Ration. Mech. Anal.
Year: 2013
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: N. Garofalo, A. Mondino
Title: Li-Yau and Harnack type inequalities in $RCD^*(K,N)$ metric measure spaces
Journal: Nonlinear Analysis TMA
Year: 2013
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Does this publication acknowledge the ERC funding? yes

Authors: N. Gigli, A. Mondino, T. Rajala
Title: Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below
Journal: J. Reine Angew. Math.
Year: 2013
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: A. Mondino
Title: A new notion of angle between three points in a metric space
Journal: Crelle's Journal
Year: 2013
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Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, A. Mondino, G. Savaré
Title: On the Bakry-Èmery condition, the gradient estimates and the Local-to-Global property of $RCD^*(K,N)$ metric measure spaces
Journal: Journal of Geometric Analysis
Year: 2014
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: F. Ferrari, A. Pinamonti
Title: Characterization by asymptotic mean formulas of q-harmonic functions in Carnot groups
Journal: Potential Analysis
Year: 2014
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Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, H. Brezis, J. Bourgain, A. Figalli
Title: $BMO$-type norms related to the perimeter of sets
Journal: Comm. Pure Appl. Math.
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, M. Colombo, A. Figalli
Title: Existence and uniqueness of maximal regular flows for non-smooth vector fields
Journal: Arch. Ration. Mech. Anal.
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, M. Colombo, A. Figalli
Title: On the Lagrangian structure of transport equations: the Vlasov-Poisson system
Journal: Duke Math. J.
Year: 2017
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Phd Thesis

Authors: S. Di Marino
Title: Recent advances on BV and Sobolev Spaces in metric measure spaces
Journal:
Year: 2014
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Preprint

Authors: L. Ambrosio, D. Trevisan
Title: Lecture notes on the DiPerna-Lions theory in abstract measure spaces
Journal:
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: V. Magnani, E. Stepanov, D. Trevisan
Title: A rough calculus approach to level sets in the Heisenberg group
Journal:
Year: 2016
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: N. Shanmugalingam, P. Lahti, L. Malý, G. Speight
Title: Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient
Journal:
Year: 2017
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Proceedings

Authors: L. Ambrosio
Title: An overview on calculus and heat flow in metric measure spaces and spaces with Riemannian curvature bounded from below
Journal:
Year: 2011
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Published Paper

Authors: L. Ambrosio, G. De Philippis, L. Martinazzi
Title: Gamma-convergence of nonlocal perimeter functionals
Journal: Manuscripta Math.
Year: 2011
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: V. Magnani
Title: An area formula in metric spaces
Journal: Colloq. Math.
Year: 2011
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, G. Da Prato, B. Goldys, D. Pallara
Title: Bounded variation with respect to a log-concave measure
Journal: Comm. P. D. E.
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, F. Ghiraldin
Title: Compactness of special functions of bounded higher variation
Journal: Analysis and Geometry in Metric Spaces
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, F. Ghiraldin
Title: Flat chains with finite size in metric spaces
Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: N. Gigli, A. Mondino
Title: A PDE approach to nonlinear potential theory in metric measure spaces
Journal: Journal de Math. Pures et Appl.
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: R. Korte, V. Magnani
Title: Measure of curves in graded groups
Journal: Illinois J. Math.
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: V. Magnani
Title: Lipschitz estimates for convex functions with respect to vector fields
Journal: Bruno Pini Mathematical Analysis Seminar
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: A. Mondino, T. Riviere
Title: Willmore Spheres in Compact Riemannian Manifolds
Journal: Advances in Math.
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: T. Ojala, T. Rajala, V. Suomala
Title: Thin and fat sets for doubling measures in metric spaces
Journal: Studia Math.
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: T. Rajala
Title: Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm
Journal: J. Funct. Anal.
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: T. Rajala
Title: Local Poincaré inequalities from stable curvature conditions on metric spaces
Journal: Calc. Var. Partial Differential Equations
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, T. Schmidt
Title: Compactness results for normal currents and the Plateau problem in dual Banach spaces
Journal: Proc. Lond. Math. Soc. (3)
Year: 2013
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: A. Bonfiglioli, E. Lanconelli, V. Magnani, M. Scienza
Title: H-convex distributions in stratified groups
Journal: Proc. Amer. Math. Soc.
Year: 2013
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: S. Mongodi
Title: Some applications of metric currents to complex analysis
Journal: Manuscripta Mathematica
Year: 2013
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: T. Rajala
Title: Improved geodesics for the reduced curvature-dimension condition in branching metric spaces
Journal: Discrete Contin. Dyn. Syst.
Year: 2013
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: T. Schmidt
Title: ${\rm W}^{2,1+\varepsilon}$ estimates for the Monge-Ampère equation
Journal: Adv. Math.
Year: 2013
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, S. Di Marino
Title: Equivalent definitions of $BV$ space and of total variation on metric measure spaces
Journal: J. Funct. Anal.
Year: 2014
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, A. Pinamonti, G. Speight
Title: Tensorization of Cheeger energies, the space $H^{1,1}$ and the area formula for graphs
Journal: Advances in Mathematics
Year: 2014
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, D. Trevisan
Title: Well posedness of Lagrangian flows and continuity equations in metric measure spaces
Journal: Analysis and PDE
Year: 2014
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: S. Di Marino, G. Speight
Title: The $p$-Weak Gradient Depends on $p$
Journal: Proceedings of the American Mathematical Society
Year: 2014
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: M. Erbar, M. Huesmann
Title: Curvature bounds for configuration space
Journal: Calculus of Variations
Year: 2014
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: V. Magnani, T. Rajala
Title: Radon-Nikodym property and area formula for Banach homogeneous group targets
Journal: Int. Math. Res. Not. IMRN
Year: 2014
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: V. Magnani, M. Scienza
Title: Characterizations of differentiability for h-convex functions in stratified groups
Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci.
Year: 2014
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: T. Schmidt
Title: Partial regularity for degenerate variational problems and image restoration models in $\rm BV$
Journal: Indiana Univ. Math. J.
Year: 2014
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: D. Vittone
Title: The regularity problem for sub-Riemannian geodesics
Journal: Geometric measure theory and real analysis, CRM Series, Ed. Norm., Pisa.
Year: 2014
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, C. De Lellis, T. Schmidt
Title: Partial regularity for mass-minimizing currents in Hilbert spaces
Journal: J. Reine Angew. Math.
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, R. Ghezzi, V. Magnani
Title: BV functions and sets of finite perimeters in sub-Riemannian manifolds
Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, M. Miranda Jr, D. Pallara
Title: Some fine properties of $BV$ functions on Wiener spaces
Journal: Anal. Geom. Metr. Spaces
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Beck, T. Schmidt
Title: Convex duality and uniqueness for $\rm BV$-minimizers
Journal: J. Funct. Anal.
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: V. Chousionis, V. Magnani, J. Tyson
Title: Removable sets for Lipschitz harmonic functions on Carnot groups
Journal: Calc. Var. Partial Differential Equations
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: V. Magnani
Title: On a measure theoretic area formula
Journal: Proc. Roy. Soc. Edinburgh Sect. A
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: V. Magnani, J. Malý, S. Mongodi
Title: A low rank property and nonexistence of higher dimensional horizontal Sobolev sets
Journal: J. Geom. Anal.
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: V. Magnani, J. Tyson, D. Vittone
Title: On transversal submanifolds and their measure
Journal: J. Anal. Math.
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: T. Schmidt
Title: Strict interior approximation of sets of finite perimeter and functions of bounded variation
Journal: Proc. Am. Math. Soc.
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: G. Speight
Title: Lusin Approximation and Horizontal Curves in Carnot Groups
Journal: Revista Matematica Iberoamericana
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: V. Magnani
Title: A new differentiation, shape of the unit ball and perimeter measure
Journal: Indiana Univ. Math. J.
Year: 2017
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: V. Magnani, A. Zapadinskaya
Title: A Gromov's dimension comparison estimate for rectifiable sets
Journal: Selecta Math. (N.S.)
Year: 2017
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Submitted Paper

Authors: L. Ambrosio, N. Gigli, G. Savaré
Title: Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
Journal:
Year: 2011
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, N. Gigli, G. Savaré
Title: Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
Journal:
Year: 2011
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, N. Gigli, G. Savaré
Title: Metric measure spaces with Riemannian Ricci curvature bounded from below
Journal:
Year: 2011
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, N. Gigli, G. Savaré
Title: Bakry-Emery curvature-dimension condition and Riemannian Ricci curvature bounds
Journal:
Year: 2012
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, S. Di Marino, G. Savaré
Title: On the duality between $p$-modulus and probability measures
Journal:
Year: 2013
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, J. Feng
Title: On a class of first order Hamilton-Jacobi equations in metric spaces
Journal:
Year: 2013
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: R. Ghezzi, F. Jean
Title: Hausdorff measures and dimensions in non equiregular sub-Riemannian manifolds
Journal:
Year: 2013
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: F. Ghiraldin
Title: Variational approximation of a functional of Mumford-Shah type in codimension higher than one
Journal: ESIAM: COCV
Year: 2013
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: S. Di Marino
Title: Sobolev and $BV$ spaces on metric measure spaces via derivations and integration by parts
Journal:
Year: 2014
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, J. Bertrand
Title: DC Calculus
Journal:
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: L. Ambrosio, M. Erbar, G. Savaré
Title: Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces
Journal:
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: S. Nardulli, A. Enrique Muñoz Flores
Title: Generalized compactness for finite perimeter sets and applications to the isoperimetric problem
Journal:
Year: 2015
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

Authors: G. Bellettini, S. Kholmatov
Title: Minimizing movements for mean curvature flow of partitions
Journal:
Year: 2017
Is open access provided to this publication? no
Does this publication acknowledge the ERC funding? yes

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