# Papers

### 2015

Ambrosio Luigi - Bertrand Jerome
DC Calculus (2015)

Ambrosio Luigi - Bourgain Jean - Brezis Haim - Figalli Alessio
$BMO$-type norms related to the perimeter of sets (2015)

Ambrosio Luigi - Colombo Maria - Figalli Alessio
Existence and uniqueness of maximal regular flows for non-smooth vector fields (2015)

Ambrosio Luigi - De Lellis Camillo - Schmidt Thomas (J. Reine Angew. Math.)
Partial regularity for mass-minimizing currents in Hilbert spaces (2015)

Ambrosio Luigi - Erbar Matthias - Savaré Giuseppe
Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces (2015)

Ambrosio Luigi - Miranda Jr Michele - Pallara Diego
Some fine properties of $BV$ functions on Wiener spaces (2015)

Ambrosio Luigi - Trevisan Dario
Lecture notes on the DiPerna-Lions theory in abstract measure spaces (2015)

Beck Lisa - Schmidt Thomas (J. Funct. Anal.)
Convex duality and uniqueness for $\rm BV$-minimizers (2015)

Beck Lisa - Schmidt Thomas (Nonlinear Anal., Theory Methods Appl.)
Interior gradient regularity for BV minimizers of singular variational problems (2015)

Enrique Muñoz Flores Abraham - Nardulli Stefano
Generalized compactness for finite perimeter sets and applications to the isoperimetric problem (2015)

Pinamonti Andrea - Speight Gareth
A Measure Zero Universal Differentiability Set in the Heisenberg Group (2015)

Schmidt Thomas (Proc. Am. Math. Soc.)
Strict interior approximation of sets of finite perimeter and functions of bounded variation (2015)

### 2014

Ambrosio Luigi - Bertrand Jerome
On the regularity of Alexandrov surfaces with curvature bounded below (2014)

Ambrosio Luigi - Colombo Maria - Figalli Alessio
On the Lagrangian structure of transport equations: the Vlasov-Poisson system (2014)

Ambrosio Luigi - Di Marino Simone (J. Funct. Anal.)
Equivalent definitions of $BV$ space and of total variation on metric measure spaces (2014)

Ambrosio Luigi - Mondino Andrea - Savaré Giuseppe
On the Bakry-Èmery condition, the gradient estimates and the Local-to-Global property of $RCD^*(K,N)$ metric measure spaces (2014)

Ambrosio Luigi - Pinamonti Andrea - Speight Gareth
Tensorization of Cheeger energies, the space $H^{1,1}$ and the area formula for graphs (2014)

Ambrosio Luigi - Pinamonti Andrea - Speight Gareth
Weighted Sobolev spaces on metric measure spaces (2014)

Ambrosio Luigi - Trevisan Dario (Analysis and PDE)
Well posedness of Lagrangian flows and continuity equations in metric measure spaces (2014)

Di Marino Simone
Recent advances on BV and Sobolev Spaces in metric measure spaces (2014)

Di Marino Simone - Speight Gareth
The $p$-Weak Gradient Depends on $p$ (2014)

Erbar Matthias - Huesmann Martin (Calculus of Variations)
Curvature bounds for configuration space (2014)

Ferrari Fausto - Pinamonti Andrea
Characterization by asymptotic mean formulas of q-harmonic functions in Carnot groups (2014)

Magnani Valentino
A new differentiation, shape of the unit ball and perimeter measure (2014)

Magnani Valentino
On a measure theoretic area formula (2014)

Scala Riccardo - Van Goethem Nicolas
Currents and dislocations at the continuum scale (2014)

Schmidt Thomas (Indiana Univ. Math. J.)
Partial regularity for degenerate variational problems and image restoration models in $\rm BV$ (2014)

Speight Gareth
Lusin Approximation and Horizontal Curves in Carnot Groups (2014)

Vittone Davide
The regularity problem for sub-Riemannian geodesics (2014)

### 2013

Ambrosio Luigi - Di Marino Simone - Savaré Giuseppe
On the duality between $p$-modulus and probability measures (2013)

Ambrosio Luigi - Feng Jin
On a class of first order Hamilton-Jacobi equations in metric spaces (2013)

Ambrosio Luigi - Ghezzi Roberta - Magnani Valentino
$BV$ functions and sets of finite perimeters in sub-Riemannian manifolds (2013)

Ambrosio Luigi - Schmidt Thomas (Proc. Lond. Math. Soc. (3))
Compactness results for normal currents and the Plateau problem in dual Banach spaces (2013)

Bonfiglioli Andrea - Lanconelli Ermanno - Magnani Valentino - Scienza Matteo (Proc. Amer. Math. Soc. )
H-convex distributions in stratified groups (2013)

Chousionis Vasilis - Magnani Valentino - Tyson Jeremy T.
Removable sets for Lipschitz harmonic functions on Carnot groups (2013)

Citti Giovanna - Manfredini Maria - Pinamonti Andrea - Serra Cassano Francesco
Poincarè type inequality for intrinsic Lipschitz continuous vector fields in the Heisenberg group (2013)

De Philippis Guido - Figalli Alessio
Higher integrability for minimizers of the Mumford-Shah functional (2013)

Garofalo Nicola - Mondino Andrea
Li-Yau and Harnack type inequalities in $RCD^*(K,N)$ metric measure spaces (2013)

Ghezzi Roberta - Jean Frédéric
Hausdorff measures and dimensions in non equiregular sub-Riemannian manifolds (2013)

Ghiraldin Francesco
Variational approximation of a functional of Mumford-Shah type in codimension higher than one (2013)

Gigli Nicola - Mondino Andrea - Rajala Tapio
Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below (2013)

Gigli Nicola - Mondino Andrea - Savaré Giuseppe
Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows (2013)

Mondino Andrea
A new notion of angle between three points in a metric space (2013)

Mongodi Samuele (Manuscripta Mathematica )
Some applications of metric currents to complex analysis (2013)

Rajala Tapio (Discrete Contin. Dyn. Syst.)
Improved geodesics for the reduced curvature-dimension condition in branching metric spaces (2013)

${\rm W}^{2,1+\varepsilon}$ estimates for the Monge-Ampère equation (2013)

### 2012

Ambrosio Luigi - Colombo Maria - De Philippis Guido - Figalli Alessio
Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case (2012)

Ambrosio Luigi - Colombo Maria - Di Marino Simone
Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope (2012)

Ambrosio Luigi - Crasta Graziano - De Cicco Virginia - De Philippis Guido
A nonautonomous chain rule in $W^{1,1}$ and in $BV$ (2012)

Ambrosio Luigi - Da Prato Giuseppe - Goldys Ben - Pallara Diego (Comm. P. D. E. )
Bounded variation with respect to a log-concave measure (2012)

Ambrosio Luigi - Figalli Alessio - Runa Eris
On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces (2012)

Ambrosio Luigi - Ghiraldin Francesco (Analysis and Geometry in Metric Spaces)
Compactness of special functions of bounded higher variation (2012)

Ambrosio Luigi - Ghiraldin Francesco (Ann. Inst. H. Poincaré Anal. Non Linéaire )
Flat chains with finite size in metric spaces (2012)

Ambrosio Luigi - Gigli Nicola - Mondino Andrea - Rajala Tapio
Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure (2012)

Ambrosio Luigi - Gigli Nicola - Savaré Giuseppe
Bakry-Emery curvature-dimension condition and Riemannian Ricci curvature bounds (2012)

Ambrosio Luigi - Rajala Tapio
Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces (2012)

De Philippis Guido - Figalli Alessio
$W^{2,1}$ regularity for solutions of the Monge-Ampère equation (2012)

Gigli Nicola - Mondino Andrea (Journal de Math. Pures et Appl.)
A PDE approach to nonlinear potential theory in metric measure spaces (2012)

Korte Riikka - Magnani Valentino (Illinois J. Math.)
Measure of curves in graded groups (2012)

Magnani Valentino (Bruno Pini Mathematical Analysis Seminar)
Lipschitz estimates for convex functions with respect to vector fields (2012)

Magnani Valentino - Malý Jan - Mongodi Samuele
A low rank property and nonexistence of higher dimensional horizontal Sobolev sets (2012)

Magnani Valentino - Rajala Tapio
Radon-Nikodym property and area formula for Banach homogeneous group targets (2012)

Magnani Valentino - Tyson Jeremy T. - Vittone Davide
On transversal submanifolds and their measure (2012)

Mondino Andrea - Nardulli Stefano
Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions (2012)

Mondino Andrea - Riviere Tristan (Advances in Math.)
Willmore Spheres in Compact Riemannian Manifolds (2012)

Mondino Andrea - Schygulla Johannes
Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds (2012)

Ojala Tuomo - Rajala Tapio - Suomala Ville (Studia Math.)
Thin and fat sets for doubling measures in metric spaces (2012)

Rajala Tapio (J. Funct. Anal.)
Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm (2012)

Rajala Tapio (Calc. Var. Partial Differential Equations)
Local Poincaré inequalities from stable curvature conditions on metric spaces (2012)

Rajala Tapio - Sturm Karl-Theodor
Non-branching geodesics and optimal maps in strong $CD(K,\infty)$-spaces (2012)

### 2011

Ambrosio Luigi - De Philippis Guido - Kirchheim Bernd
Regularity of optimal transport maps and partial differential inclusions (2011)

Ambrosio Luigi - De Philippis Guido - Martinazzi Luca (Manuscripta Math.)
Gamma-convergence of nonlocal perimeter functionals (2011)

Ambrosio Luigi - Figalli Alessio - Friesecke Gero - Giannoulis Johannes - Paul Thierry
Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data (2011)

Ambrosio Luigi - Gigli Nicola - Savaré Giuseppe
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below (2011)

Ambrosio Luigi - Gigli Nicola - Savaré Giuseppe
Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces (2011)

Ambrosio Luigi - Gigli Nicola - Savaré Giuseppe
Metric measure spaces with Riemannian Ricci curvature bounded from below (2011)

Magnani Valentino (Colloq. Math.)
An area formula in metric spaces (2011)

Mondino Andrea - Riviere Tristan
Immersed Spheres of Finite Total Curvature into Manifolds (2011)

### 2010

Ambrosio Luigi - Figalli Alessio
Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces (2010)

Magnani Valentino - Scienza Matteo
Characterizations of differentiability for h-convex functions in stratified groups (2010)