206 citations · 1.5k across the 62 of their papers we have counts for
11 papers · 1 filter
Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
Nicola Gigli, Andrea Mondino, Giuseppe Savaré
Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equi…
Concentration of small Willmore spheres in Riemannian 3-manifolds
Paul Laurain, Andrea Mondino
Given a 3-dimensional Riemannian manifold , we prove that if is a sequence of Willmore spheres (or more generally area-constrained Willmore spheres), having Willmore…
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…
A Gap Theorem for Willmore Tori and an application to the Willmore Flow
Andrea Mondino, Huy The Nguyen
In 1965 Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in is at least and attains this minimal value if and only if the…
A frame energy for immersed tori and applications to regular homotopy classes
Andrea Mondino, Tristan Rivière
The paper is devoted to study the Dirichelet energy of moving frames on 2-dimensional tori immersed in the euclidean -dimensional space. This functional, called Frame ener…
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…
Immersed Spheres of Finite Total Curvature into Manifolds
Andrea Mondino, Tristan Rivière
We prove that a sequence of possibly branched, weak immersions of the two-sphere into an arbitrary compact riemannian manifold with uniformly bounded area and unifo…
Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint
Laura Gioia Andrea Keller, Andrea Mondino, Tristan Rivière
The isoperimetric ratio of an embedded surface in is defined as the ratio of the area of the surface to power three to the squared enclosed volume. The aim of the present wor…
Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below
Nicola Gigli, Andrea Mondino, Tapio Rajala
We show that in any infinitesimally Hilbertian -space at almost every point there exists a Euclidean weak tangent, i.e. there exists a sequence of dilations of the space…
Existence of generalized totally umbilic 2-spheres in perturbed 3-spheres
Alessandro Carlotto, Andrea Mondino
It was recently shown by R. Souam and E. Toubiana that the (non constantly curved) Berger spheres do not contain totally umbilic surfaces. Nevertheless in this article we show, by…
A new notion of angle between three points in a metric space
Andrea Mondino
We give a new notion of angle in general metric spaces; more precisely, given a triple a points in a metric space , we introduce the notion of angle cone ${\angle_{p…