Sharp log-Sobolev inequalities in CD(0,N) spaces with applications

Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

(2023) Gioacchino Antonelli et al.   MATHEMATISCHE ANNALEN

Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature

(2022) Zoltán M. Balogh et al.   MATHEMATISCHE ANNALEN

Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds

(2022) Francesco Nobili et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Sobolev Inequalities in Manifolds with Nonnegative Curvature

(2022) Simon Brendle   COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

Minimising hulls, p-capacity and isoperimetric inequality on complete Riemannian manifolds

(2022) Mattia Fogagnolo et al.   JOURNAL OF FUNCTIONAL ANALYSIS

The globalization theorem for the Curvature-Dimension condition

(2021) Fabio Cavalletti et al.   INVENTIONES MATHEMATICAE

Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature

(2020) Virginia Agostiniani et al.   INVENTIONES MATHEMATICAE

Polya-Szego inequality and Dirichlet p-spectral gap for non-smooth spaces with Ricci curvature bounded below

(2019) Andrea Mondino et al.   JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

(2019) Luigi Ambrosio et al.   MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY

Lecture Notes On Differential Calculus on $\mathscr {RCD}$ Spaces

(2018) Nicola Gigli   PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES

Perimeter as relaxed Minkowski content in metric measure spaces

(2017) Luigi Ambrosio et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Metric measure spaces supporting Gagliardo–Nirenberg inequalities: volume non-collapsing and rigidities

(2016) Alexandru Kristály   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

From volume cone to metric cone in the nonsmooth setting

(2016) Guido De Philippis et al.   GEOMETRIC AND FUNCTIONAL ANALYSIS

Cones over metric measure spaces and the maximal diameter theorem

(2015) Christian Ketterer   JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

On the differential structure of metric measure spaces and applications

(2015) Nicola Gigli   MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY

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

Hamilton Jacobi equations on metric spaces and transport entropy inequalities

(2014) Nathael Gozlan et al.   REVISTA MATEMATICA IBEROAMERICANA

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

Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm

(2012) Tapio Rajala   JOURNAL OF FUNCTIONAL ANALYSIS

An optimal logarithmic Sobolev inequality with Lipschitz constants

(2011) Yasuhiro Fujita   JOURNAL OF FUNCTIONAL ANALYSIS

Ricci curvature for metric-measure spaces via optimal transport

(2009) John Lott et al.   ANNALS OF MATHEMATICS

Mass Transport and Variants of the Logarithmic Sobolev Inequality

(2008) Franck Barthe et al.   JOURNAL OF GEOMETRIC ANALYSIS