206 citations · 1.5k across the 62 of their papers we have counts for
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Nonlinear diffusion equations and curvature conditions in metric measure spaces
Luigi Ambrosio, Andrea Mondino, Giuseppe Savaré
Aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, our new approach…
Homotopy properties of horizontal loop spaces and applications to closed sub-riemannian geodesics
Antonio Lerario, Andrea Mondino
Given a manifold and a proper sub-bundle , we study homotopy properties of the horizontal base-point free loop space , i.e. the space of absolutely continuous m…
Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds
Fabio Cavalletti, Andrea Mondino
For metric measure spaces verifying the reduced curvature-dimension condition we prove a series of sharp functional inequalities under the additional assumption of esse…
Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds
Fabio Cavalletti, Andrea Mondino
We prove that if is a metric measure space with having (in a synthetic sense) Ricci curvature bounded from below by and dime…
Global Conformal Invariants of Submanifolds
Andrea Mondino, Huy The Nguyen
The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of g…
Measure rigidity of Ricci curvature lower bounds
Fabio Cavalletti, Andrea Mondino
The measure contraction property, for short, is a weak Ricci curvature lower bound conditions for metric measure spaces. The goal of this paper is to understand whic…