L. Ambrosio:
An overview on calculus and heat flow in metric measure spaces and spaces with Riemannian curvature bounded from below
(Proceedings) 2011
L. Ambrosio, J. Bertrand:
DC Calculus
(Submitted Paper) 2015
L. Ambrosio, J. Bourgain, H. Brezis, A. Figalli:
$BMO$-type norms related to the perimeter of sets
Comm. Pure Appl. Math. (Accepted Paper) 2015
L. Ambrosio, M. Colombo, G. De Philippis, A. Figalli:
Existence of Eulerian solutions to the semigeostrophic equations in
physical space: the 2-dimensional periodic case
Comm. Partial Differential Equations (Accepted Paper) 2012
L. Ambrosio, M. Colombo, S. Di Marino:
Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope
Advanced Studies in Pure Mathematics: "Variational methods for evolving objects" (Accepted Paper) Vol. 67, p. 1-58, 2012
L. Ambrosio, M. Colombo, A. Figalli:
Existence and uniqueness of maximal regular flows for non-smooth vector fields
Arch. Ration. Mech. Anal. (Accepted Paper) 2015
L. Ambrosio, M. Colombo, A. Figalli:
On the Lagrangian structure of transport equations: the Vlasov-Poisson system
Duke Math. J. (Accepted Paper) 2017
L. Ambrosio, G. Crasta, V. De Cicco, G. De Philippis:
A nonautonomous chain rule in $W^{1,p}$ and in $BV$
Manuscripta Math. (Accepted Paper) 2012
L. Ambrosio, G. Da Prato, B. Goldys, D. Pallara:
Bounded variation with respect to a log-concave measure
Comm. P. D. E. Vol. 37, p. 2272-2290, 2012
L. Ambrosio, C. De Lellis, T. Schmidt:
Partial regularity for mass-minimizing currents in Hilbert spaces
J. Reine Angew. Math. Vol. 734, p. 99-144, 2018
L. Ambrosio, G. De Philippis, B. Kirchheim:
Regularity of optimal transport maps and partial differential inclusions
Rend. Lincei - Mat. e Appl. () 2011
L. Ambrosio, G. De Philippis, L. Martinazzi:
Gamma-convergence of nonlocal perimeter functionals
Manuscripta Math. Vol. 134, p. 377-403, 2011
L. Ambrosio, S. Di Marino:
Equivalent definitions of $BV$ space and of total variation on metric measure spaces
J. Funct. Anal. Vol. 266, N. 7, p. 4150-4188, 2014
L. Ambrosio, S. Di Marino, G. Savaré:
On the duality between $p$-modulus and probability measures
(Submitted Paper) 2013
L. Ambrosio, M. Erbar, G. Savaré:
Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces
(Submitted Paper) 2015
L. Ambrosio, J. Feng:
On a class of first order Hamilton-Jacobi equations in metric spaces
(Submitted Paper) 2013
L. Ambrosio, A. Figalli:
Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces
Ann. Fac. Sci. Toulouse Math. (Accepted Paper) 2010
L. Ambrosio, A. Figalli, G. Friesecke, J. Giannoulis, T. Paul:
Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data
Comm. Pure Appl. Math. (Accepted Paper) 2011
L. Ambrosio, A. Figalli, E. Runa:
On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. (Accepted Paper) 2012
L. Ambrosio, R. Ghezzi, V. Magnani:
BV functions and sets of finite perimeters in sub-Riemannian manifolds
Ann. Inst. H. Poincaré Anal. Non Linéaire Vol. 32, N. 3, p. 489517, 2015
L. Ambrosio, F. Ghiraldin:
Compactness of special functions of bounded higher variation
Analysis and Geometry in Metric Spaces Vol. 1, p. 130, 2012
L. Ambrosio, F. Ghiraldin:
Flat chains with finite size in metric spaces
Ann. Inst. H. Poincaré Anal. Non Linéaire 2012
L. Ambrosio, N. Gigli, A. Mondino, T. Rajala:
Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure
Transactions of the AMS (Accepted Paper) 2012
L. Ambrosio, N. Gigli, G. Savaré:
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
(Submitted Paper) 2011
L. Ambrosio, N. Gigli, G. Savaré:
Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
(Submitted Paper) 2011
L. Ambrosio, N. Gigli, G. Savaré:
Metric measure spaces with Riemannian Ricci curvature bounded from below
(Submitted Paper) 2011
L. Ambrosio, N. Gigli, G. Savaré:
Bakry-Emery curvature-dimension condition and Riemannian Ricci curvature bounds
(Submitted Paper) 2012
L. Ambrosio, M. Miranda Jr, D. Pallara:
Some fine properties of $BV$ functions on Wiener spaces
Anal. Geom. Metr. Spaces Vol. 3, p. 23-48, 2015
L. Ambrosio, A. Mondino, G. Savaré:
On the Bakry-Èmery condition, the gradient estimates and the Local-to-Global property of $RCD^*(K,N)$ metric measure spaces
Journal of Geometric Analysis (Accepted Paper) 2014
L. Ambrosio, A. Pinamonti, G. Speight:
Tensorization of Cheeger energies, the space $H^{1,1}$ and the area formula for graphs
Advances in Mathematics Vol. 281, N. 1145-1177, 2014
L. Ambrosio, T. Rajala:
Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces
Ann. Mat. Pura Appl. (Accepted Paper) 2012
L. Ambrosio, T. Schmidt:
Compactness results for normal currents and the Plateau problem in dual Banach spaces
Proc. Lond. Math. Soc. (3) Vol. 106, N. 5, p. 1121-1142, 2013
L. Ambrosio, D. Trevisan:
Well posedness of Lagrangian flows and continuity equations in metric
measure spaces
Analysis and PDE Vol. 7, N. 5, p. 1179-1234, 2014
L. Ambrosio, D. Trevisan:
Lecture notes on the DiPerna-Lions theory in abstract measure spaces
(Preprint) 2015
L. Beck, T. Schmidt:
Convex duality and uniqueness for $\rm BV$-minimizers
J. Funct. Anal. Vol. 268, N. 10, p. 3061-3107, 2015
G. Bellettini, S. Kholmatov:
Minimizing movements for mean curvature flow of partitions
(Submitted Paper) 2017
A. Bonfiglioli, E. Lanconelli, V. Magnani, M. Scienza:
H-convex distributions in stratified groups
Proc. Amer. Math. Soc. Vol. 141, N. 10, p. 3633-3638, 2013
V. Chousionis, V. Magnani, J. Tyson:
Removable sets for Lipschitz harmonic functions on Carnot groups
Calc. Var. Partial Differential Equations Vol. 53, N. 3-4, p. 755780, 2015
G. Citti, M. Manfredini, A. Pinamonti, F. Serra Cassano:
Poincaré-type inequality for Lipschitz continuous vector fields
JMPA (Accepted Paper) 2013
G. De Philippis, A. Figalli:
$W^{2,1}$ regularity for solutions of the Monge-Ampère equation
Invent. Math. (Accepted Paper) 2012
G. De Philippis, A. Figalli:
Higher integrability for minimizers of the Mumford-Shah functional
Arch. Ration. Mech. Anal. (Accepted Paper) 2013
S. Di Marino:
Recent advances on BV and Sobolev Spaces in metric measure spaces
(Phd Thesis) 2014
S. Di Marino:
Sobolev and $BV$ spaces on metric measure spaces via derivations and integration by parts
(Submitted Paper) 2014
S. Di Marino, G. Speight:
The $p$-Weak Gradient Depends on $p$
Proceedings of the American Mathematical Society Vol. 143, N. 5239-5252, 2014
A. Enrique Muñoz Flores, S. Nardulli:
Generalized compactness for finite perimeter sets and applications to the isoperimetric problem
(Submitted Paper) 2015
M. Erbar, M. Huesmann:
Curvature bounds for configuration space
Calculus of Variations 2014
F. Ferrari, A. Pinamonti:
Characterization by asymptotic mean formulas of q-harmonic functions in Carnot groups
Potential Analysis (Accepted Paper) 2014
N. Garofalo, A. Mondino:
Li-Yau and Harnack type inequalities in $RCD^*(K,N)$ metric measure spaces
Nonlinear Analysis TMA (Accepted Paper) 2013
R. Ghezzi, F. Jean:
Hausdorff measures and dimensions in non equiregular sub-Riemannian manifolds
(Submitted Paper) 2013
F. Ghiraldin:
Variational approximation of a functional of Mumford-Shah type in codimension higher than one
ESIAM: COCV (Submitted Paper) 2013
N. Gigli, A. Mondino:
A PDE approach to nonlinear potential theory in metric measure spaces
Journal de Math. Pures et Appl. 2012
N. Gigli, A. Mondino, T. Rajala:
Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below
J. Reine Angew. Math. (Accepted Paper) 2013
R. Jones, P. Lahti, N. Shanmugalingam:
Modulus of families of sets of finite perimeter and quasiconformal maps between metric spaces of globally $Q$-bounded geometry
(Preprint) p. 26, 2018
R. Korte, V. Magnani:
Measure of curves in graded groups
Illinois J. Math. Vol. 56, N. 2, p. 353-366, 2012
P. Lahti, L. Malý, N. Shanmugalingam, G. Speight:
Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient
(Preprint) 2017
V. Magnani:
An area formula in metric spaces
Colloq. Math. Vol. 124, p. 275-283, 2011
V. Magnani:
Lipschitz estimates for convex functions with respect to vector fields
Bruno Pini Mathematical Analysis Seminar Vol. 1, p. 60-71, 2012
V. Magnani:
On a measure theoretic area formula
Proc. Roy. Soc. Edinburgh Sect. A Vol. 145, p. 885-891, 2015
V. Magnani:
A new differentiation, shape of the unit ball and perimeter measure
Indiana Univ. Math. J. Vol. 66, N. 1, p. 183-204, 2017
V. Magnani, J. Malý, S. Mongodi:
A low rank property and nonexistence of higher dimensional horizontal Sobolev sets
J. Geom. Anal. Vol. 25, N. 3, p. 14441458, 2015
V. Magnani, T. Rajala:
Radon-Nikodym property and area formula for Banach homogeneous group targets
Int. Math. Res. Not. IMRN Vol. 23, p. 63996430, 2014
V. Magnani, M. Scienza:
Characterizations of differentiability for h-convex functions in stratified groups
Ann. Scuola Norm. Sup. Pisa Cl. Sci. Vol. 13, p. 675-697, 2014
V. Magnani, E. Stepanov, D. Trevisan:
A rough calculus approach to level sets in the Heisenberg group
J. London Math. Soc. (Accepted Paper) 2016
V. Magnani, J. Tyson, D. Vittone:
On transversal submanifolds and their measure
J. Anal. Math. Vol. 125, p. 319351, 2015
V. Magnani, A. Zapadinskaya:
A Gromov's dimension comparison estimate for rectifiable sets
Selecta Math. (N.S.) Vol. 23, N. 2, p. 1153-1174, 2017
A. Mondino:
A new notion of angle between three points in a metric space
Crelle's Journal (Accepted Paper) 2013
A. Mondino, S. Nardulli:
Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions
Communications in Analysis and Geometry (Accepted Paper) p. 17, 2012
A. Mondino, T. Riviere:
Immersed Spheres of Finite Total Curvature into Manifolds
Advances in Calc. Var. (Accepted Paper) p. 33, 2011
A. Mondino, T. Riviere:
Willmore Spheres in Compact Riemannian Manifolds
Advances in Math. p. 58, 2012
A. Mondino, J. Schygulla:
Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds
Annales IHP-Anal. Non Lin. (Accepted Paper) p. 19, 2012
S. Mongodi:
Some applications of metric currents to complex analysis
Manuscripta Mathematica Vol. 141, N. 3-4, p. pp 363-390, 2013
T. Ojala, T. Rajala, V. Suomala:
Thin and fat sets for doubling measures in metric spaces
Studia Math. Vol. 208, p. 195-211, 2012
T. Rajala:
Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm
J. Funct. Anal. Vol. 263, N. 4, p. 896-924, 2012
T. Rajala:
Local Poincaré inequalities from stable curvature conditions on metric spaces
Calc. Var. Partial Differential Equations Vol. 44, N. 3-4, p. 477-494, 2012
T. Rajala:
Improved geodesics for the reduced curvature-dimension condition in branching metric spaces
Discrete Contin. Dyn. Syst. Vol. 33, N. 7, p. 3043 - 3056, 2013
T. Rajala, K. T. Sturm:
Non-branching geodesics and optimal maps in strong $CD(K,\infty)$-spaces
Calc. Var. Partial Differential Equations (Accepted Paper) 2012
T. Schmidt:
${\rm W}^{2,1+\varepsilon}$ estimates for the Monge-Ampère equation
Adv. Math. Vol. 240, p. 672-689, 2013
T. Schmidt:
Partial regularity for degenerate variational problems and image restoration models in $\rm BV$
Indiana Univ. Math. J. Vol. 63, N. 1, p. 213-279, 2014
T. Schmidt:
Strict interior approximation of sets of finite perimeter and functions of bounded variation
Proc. Am. Math. Soc. Vol. 143, N. 5, p. 2069-2084, 2015
G. Speight:
Lusin Approximation and Horizontal Curves in Carnot Groups
Revista Matematica Iberoamericana Vol. 32, N. 4, p. 1425-1446, 2015
D. Vittone:
The regularity problem for sub-Riemannian geodesics
Geometric measure theory and real analysis, CRM Series, Ed. Norm., Pisa. Vol. 17, p. 193--226, 2014