L. Ambrosio, G. De Philippis, B. Kirchheim:
Regularity of optimal transport maps and partial differential inclusions
Rend. Lincei - Mat. e Appl. () 2011
A. Mondino, T. Rivière:
Immersed Spheres of Finite Total Curvature into Manifolds
Advances in Calc. Var. (Accepted Paper) p. 33, 2011
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, 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, 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, T. Rajala:
Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces
Ann. Mat. Pura Appl. (Accepted Paper) 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
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
G. Citti, M. Manfredini, A. Pinamonti, F. Serra Cassano:
Poincaré-type inequality for Lipschitz continuous vector fields
JMPA (Accepted Paper) 2013
N. Garofalo, A. Mondino:
Li-Yau and Harnack type inequalities in $RCD^*(K,N)$ metric measure spaces
Nonlinear Analysis TMA (Accepted Paper) 2013
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
A. Mondino:
A new notion of angle between three points in a metric space
Crelle's Journal (Accepted Paper) 2013
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
F. Ferrari, A. Pinamonti:
Characterization by asymptotic mean formulas of q-harmonic functions in Carnot groups
Potential Analysis (Accepted Paper) 2014
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
Journal of Geometric Analysis (Accepted Paper) 2018
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
Indiana University Math. J. (Accepted Paper) 2019
S. Di Marino:
Recent advances on BV and Sobolev Spaces in metric measure spaces
(Phd Thesis) 2014
L. Ambrosio, D. Trevisan:
Lecture notes on the DiPerna-Lions theory in abstract measure spaces
(Preprint) 2015
S. Eriksson-Bique, J. Gill, P. Lahti, N. Shanmugalingam:
Asymptotic behavior of BV functions and sets of finite perimeter in metric measure spaces
(Preprint) 2018
Q. Liu, N. Shanmugalingam, X. Zhou:
Equivalence of solutions of eikonal equation in metric spaces
(Preprint) 2020
G. Bellettini, S. Kholmatov:
Some aspects of anisotropic curvature flow of planar partitions
(Preprint) 2023
F. Almuratov, G. Bellettini, S. Kholmatov:
Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions
(Preprint) 2024
G. Bellettini, S. Kholmatov:
Minimizing movements for the generalized power mean curvature flow
(Preprint) 2024
S. Kholmatov:
Consistency of minimizing movements with smooth mean curvature flow of droplets with prescribed contact-angle in $\mathbb R^3$
(Preprint) 2024
S. Kholmatov:
Minimizing movements for forced anisotropic curvature flow of droplets
(Preprint) 2024
S. Kholmatov:
On the minimality of the Winterbottom shape
(Preprint) 2024
L. Ambrosio:
An overview on calculus and heat flow in metric measure spaces and spaces with Riemannian curvature bounded from below
(Proceedings) 2011
N. Shanmugalingam:
$p$-hyperbolicity of ends and families of paths in metric spaces
(Proceedings) 2019
L. Ambrosio, G. De Philippis, L. Martinazzi:
Gamma-convergence of nonlocal perimeter functionals
Manuscripta Math. Vol. 134, p. 377-403, 2011
L. Ambrosio, A. Figalli:
Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces
Ann. Fac. Sci. Toulouse Math. 2011
V. Magnani:
An area formula in metric spaces
Colloq. Math. Vol. 124, p. 275-283, 2011
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 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, 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
N. Gigli, A. Mondino:
A PDE approach to nonlinear potential theory in metric measure spaces
Journal de Math. Pures et Appl. 2012
R. Korte, V. Magnani:
Measure of curves in graded groups
Illinois J. Math. Vol. 56, N. 2, p. 353-366, 2012
V. Magnani:
Lipschitz estimates for convex functions with respect to vector fields
Bruno Pini Mathematical Analysis Seminar Vol. 1, p. 60-71, 2012
A. Mondino, S. Nardulli:
Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions
Communications in Analysis and Geometry p. 17, 2012
A. Mondino, T. Rivière:
Willmore Spheres in Compact Riemannian Manifolds
Advances in Math. p. 58, 2012
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
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. 2013
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
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
G. De Philippis, A. Figalli:
$W^{2,1}$ regularity for solutions of the Monge-Ampère equation
Invent. Math. 2013
S. Mongodi:
Some applications of metric currents to complex analysis
Manuscripta Mathematica Vol. 141, N. 3-4, p. pp 363-390, 2013
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. Schmidt:
${\rm W}^{2,1+\varepsilon}$ estimates for the Monge-Ampère equation
Adv. Math. Vol. 240, p. 672-689, 2013
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, 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, 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
G. De Philippis, A. Figalli:
Higher integrability for minimizers of the Mumford-Shah functional
Arch. Ration. Mech. Anal. 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
M. Erbar, M. Huesmann:
Curvature bounds for configuration space
Calculus of Variations 2014
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
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
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
L. Ambrosio, M. Colombo, A. Figalli:
Existence and uniqueness of maximal regular flows for non-smooth vector fields
Arch. Ration. Mech. Anal. 2015
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, 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. Beck, T. Schmidt:
Convex duality and uniqueness for $\rm BV$-minimizers
J. Funct. Anal. Vol. 268, N. 10, p. 3061-3107, 2015
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
V. Magnani:
On a measure-theoretic area formula
Proc. Roy. Soc. Edinburgh Sect. A Vol. 145, p. 885-891, 2015
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, J. T. Tyson, D. Vittone:
On transversal submanifolds and their measure
J. Anal. Math. Vol. 125, p. 319351, 2015
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
L. Ambrosio, J. Bourgain, H. Brezis, A. Figalli:
$BMO$-type norms related to the perimeter of sets
Comm. Pure Appl. Math. 2016
L. Ambrosio, M. Colombo, A. Figalli:
On the Lagrangian structure of transport equations: the Vlasov-Poisson system
Duke Math. J. 2017
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, A. Zapadinskaya:
A Gromov's dimension comparison estimate for rectifiable sets
Selecta Math. (N.S.) Vol. 23, N. 2, p. 1153-1174, 2017
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
S. Nardulli, P. Pansu:
A complete Riemannian manifold whose isoperimetric profile is discontinuous
Annali della Scuola Normale Superiore di Pisa Classe di Scienze Vol. XVII, N. 2, p. 12, 2018
S. Nardulli, F. Russo:
On the Hamilton's isoperimetric ratio in complete Riemannian manifolds of finite volume
Journal of Functional Analysis Vol. 280, N. 4, p. 29(ArXiv Version), 2021
A. Enrique Muñoz Flores, S. Nardulli:
Generalized compactness for finite perimeter sets and applications to the isoperimetric problem
Journal of Dynamical and Control Systems Vol. 28, p. 5969, 2022
R. Resende:
On clusters and the multi-isoperimetric profile in Riemannian manifolds with bounded geometry
Journal of Dynamical and Control Systems p. 23, 2022
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, S. Di Marino, G. Savaré:
On the duality between p-Modulus and probability measures
(Submitted Paper) 2013
L. Ambrosio, J. Feng:
On a class of first order Hamilton-Jacobi equations in metric spaces
(Submitted 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
S. Di Marino:
Sobolev and BV spaces on metric measure spaces via derivations and
integration by parts
(Submitted Paper) 2014
L. Ambrosio, J. Bertrand:
DC Calculus
(Submitted Paper) 2015
L. Ambrosio, M. Erbar, G. Savaré:
Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces
(Submitted Paper) 2015
G. Bellettini, S. Kholmatov:
Minimizing movements for mean curvature flow of partitions
(Submitted Paper) 2017
G. Bellettini, A. Chambolle, S. Kholmatov:
Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities
(Submitted Paper) 2020
R. Resende :
On clusters and the multi-isoperimetric profile in Riemannian manifolds with bounded geometry
(Submitted Paper) p. 22, 2020
G. Foghem, M. Kassmann:
A general framework for nonlocal Neumann problems
(preprint) 2022