Isoperimetric sets in spaces with lower bounds on the Ricci curvature

Boundary regularity and stability for spaces with Ricci bounded below

(2022) Elia Bruè et al.   INVENTIONES MATHEMATICAE

Rectifiability of the reduced boundary for sets of finite perimeter over $\operatorname{RCD}(K,N)$ spaces

(2022) Elia Bruè et al.   JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

On the topology and the boundary of N–dimensional RCD(K,N) spaces

(2021) Vitali Kapovitch et al.   GEOMETRY & TOPOLOGY

The globalization theorem for the Curvature-Dimension condition

(2021) Fabio Cavalletti et al.   INVENTIONES MATHEMATICAE

On BV functions and essentially bounded divergence-measure fields in metric spaces

(2021) Vito Buffa et al.   REVISTA MATEMATICA IBEROAMERICANA

The ε - εβ Property in the Isoperimetric Problem with Double Density, and the Regularity of Isoperimetric Sets

(2020) Aldo Pratelli et al.   ADVANCED NONLINEAR STUDIES

Indecomposable sets of finite perimeter in doubling metric measure spaces

(2020) Paolo Bonicatto et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifolds

(2020) Bang-Xian Han   ADVANCES IN MATHEMATICS

A sharp Leibniz rule for BV functions in metric spaces

(2019) Panu Lahti   Revista Matematica Complutense

Almost Euclidean Isoperimetric Inequalities in Spaces Satisfying Local Ricci Curvature Lower Bounds

(2018) Fabio Cavalletti et al.   INTERNATIONAL MATHEMATICS RESEARCH NOTICES

Sharp Isoperimetric Inequalities for Small Volumes in Complete Noncompact Riemannian Manifolds of Bounded Geometry Involving the Scalar Curvature

(2018) Stefano Nardulli et al.   INTERNATIONAL MATHEMATICS RESEARCH NOTICES

Quasiopen Sets, Bounded Variation and Lower Semicontinuity in Metric Spaces

(2018) Panu Lahti   POTENTIAL ANALYSIS

Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma $-finite measure

(2015) Luigi Ambrosio et al.   TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Generalized existence of isoperimetric regions in non-compact Riemannian manifolds and applications to the isoperimetric profile

(2014) Stefano Nardulli   Asian Journal of Mathematics

Metric measure spaces with Riemannian Ricci curvature bounded from below

(2014) Luigi Ambrosio et al.   DUKE MATHEMATICAL JOURNAL

On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces

(2014) Matthias Erbar et al.   INVENTIONES MATHEMATICAE

Equivalent definitions of BV space and of total variation on metric measure spaces

(2014) Luigi Ambrosio et al.   JOURNAL OF FUNCTIONAL ANALYSIS

Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in $RCD (K, \infty)$ metric measure spaces

(2013) Giuseppe Savaré   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

(2013) Luigi Ambrosio et al.   INVENTIONES MATHEMATICAE

Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces

(2013) Luigi Ambrosio et al.   REVISTA MATEMATICA IBEROAMERICANA

Regularity of Sets with Quasiminimal Boundary Surfaces in Metric Spaces

(2012) Juha Kinnunen et al.   JOURNAL OF GEOMETRIC ANALYSIS

Existence of isoperimetric regions in contact sub-Riemannian manifolds

(2012) Matteo Galli et al.   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Local Poincaré inequalities from stable curvature conditions on metric spaces

(2011) Tapio Rajala   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Ricci curvature for metric-measure spaces via optimal transport

(2009) John Lott et al.   ANNALS OF MATHEMATICS