206 citations · 1.5k across the 62 of their papers we have counts for
6 papers · 1 filter
A Talenti-type comparison theorem for spaces and applications
Andrea Mondino, Mattia Vedovato
We prove pointwise and -gradient comparison results for solutions to elliptic Dirichlet problems defined on open subsets of a (possibly non-smooth) space with positive Ricci…
On a isoperimetric-isodiametric inequality
Andrea Mondino, Emanuele Spadaro
The Euclidean mixed isoperimetric-isodiametric inequality states that the round ball maximizes the volume under constraint on the product between boundary area and radius. The goal…
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…
On the Bakry-Émery condition, the gradient estimates and the Local-to-Global property of RCD*(K,N) metric measure spaces
Luigi Ambrosio, Andrea Mondino, Giuseppe Savaré
We prove higher summability and regularity of Γ(f) for functions f in spaces satisfying the Bakry-Émery condition BE(K,\infty). As a byproduct, we obtain various equivalent weak fo…
Li-Yau and Harnack type inequalities in metric measure spaces
Nicola Garofalo, Andrea Mondino
Metric measure spaces satisfying the reduced curvature-dimension condition and where the heat flow is linear are called -spaces. This class of non smooth sp…
Willmore Spheres in Compact Riemannian Manifolds
Andrea Mondino, Tristan Rivière
The paper is devoted to the variational analysis of the Willmore, and other L^2 curvature functionals, among immersions of 2-dimensional surfaces into a compact riemannian m-manifo…