206 citations · 1.5k across the 62 of their papers we have counts for
33 papers · 1 filter
Orientability of metric manifolds and metric spaces with curvature bounds
Nicola Cavallucci, Denis Marti, Andrea Mondino +1
We develop a theory of orientability for metric manifolds and singular metric spaces using locally integral currents. For topological -manifolds with locally finite Hausdorff me…
Gromov-Hausdorff and intrinsic flat convergence of RCD(K,N) and Kato spaces
Andrea Mondino, Raquel Perales
We consider metric measure spaces satisfying the properties (ETR), (LBD), and with an almost everywhere connected regular set. In particular, these a…
On the geometry of synthetic null hypersurfaces
Fabio Cavalletti, Davide Manini, Andrea Mondino
This paper develops a synthetic framework for the geometric and analytic study of null (lightlike) hypersurfaces in non-smooth spacetimes. Drawing from optimal transport and recent…
Optimal transport on null hypersurfaces and the null energy condition
Fabio Cavalletti, Davide Manini, Andrea Mondino
The goal of the present work is to study optimal transport on null hypersurfaces inside Lorentzian manifolds. The challenge here is that optimal transport along a null hypersurface…
Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from spaces to spaces
Andrea Mondino, Daniele Semola
We establish Lipschitz regularity of harmonic maps from metric measure spaces with lower Ricci curvature bounds and dimension upper bounds in synthetic sense wi…
A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces
Mustafa Alper Gunes, Andrea Mondino
In the framework of (possibly non-smooth) metric measure spaces with Ricci curvature bounded below by a positive constant in a synthetic sense, we establish a sharp and rigid rever…
Weak Laplacian bounds and minimal boundaries in non-smooth spaces with Ricci curvature lower bounds
Andrea Mondino, Daniele Semola
The goal of the paper is four-fold. In the setting of non-smooth spaces with Ricci curvature lower bounds (more precisely RCD(K,N) metric measure spaces): - we develop an intrinsic…
Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity
Andrea Mondino, Aidan Templeton-Browne
We prove rigidity results involving the Hawking mass for surfaces immersed in a -dimensional, complete Riemannian manifold with non-negative scalar curvature (resp. with…
An upper bound on the revised first Betti number and a torus stability result for RCD spaces
Ilaria Mondello, Andrea Mondino, Raquel Perales
We prove an upper bound on the rank of the abelianised revised fundamental group (called "revised first Betti number") of a compact space, in the same spirit of the…
A strict inequality for the minimisation of the Willmore functional under isoperimetric constraint
Andrea Mondino, Christian Scharrer
Inspired by previous work of Kusner and Bauer-Kuwert, we prove a strict inequality between the Willmore energies of two surfaces and their connected sum in the context of isoperime…
Existence and Regularity of Spheres Minimising the Canham-Helfrich Energy
Andrea Mondino, Christian Scharrer
We prove existence and regularity of minimisers for the Canham-Helfrich energy in the class of weak (possibly branched and bubbled) immersions of the -sphere. This solves (the s…
Foliation by area-constrained Willmore spheres near a non-degenerate critical point of the scalar curvature
Norihisa Ikoma, Andrea Malchiodi, Andrea Mondino
Let be a 3-dimensional Riemannian manifold. The goal of the paper it to show that if is a non-degenerate critical point of the scalar curvature, then a neighbo…
Quantitative isoperimetry à la Levy-Gromov
F. Cavalletti, F. Maggi, A. Mondino
On a Riemannian manifold with a positive lower bound on the Ricci tensor, the distance of isoperimetric sets from geodesic balls is quantitatively controlled in terms of the gap be…
Almost euclidean Isoperimetric Inequalities in spaces satisfying local Ricci curvature lower bounds
Fabio Cavalletti, Andrea Mondino
Motivated by Perelman's Pseudo Locality Theorem for the Ricci flow, we prove that if a Riemannian manifold has Ricci curvature bounded below in a metric ball which moreover has alm…
Rigidity for critical points in the Levy-Gromov inequality
Fabio Cavalletti, Francesco Maggi, Andrea Mondino
The Levy-Gromov inequality states that round spheres have the least isoperimetric profile (normalized by total volume) among Riemannian manifolds with a fixed positive lower bound…
Sectional and intermediate Ricci curvature lower bounds via Optimal Transport
Christian Ketterer, Andrea Mondino
The goal of the paper is to give an optimal transport characterization of sectional curvature lower (and upper) bounds for smooth -dimensional Riemannian manifolds. More general…
A non-existence result for minimal catenoids in asymptotically flat spaces
Alessandro Carlotto, Andrea Mondino
We show that asymptotically Schwarzschildean 3-manifolds cannot contain minimal surfaces obtained by perturbative deformations of a Euclidean catenoid, no matter how small the ADM…
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…
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…
Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds I: Minimization
Norihisa Ikoma, Andrea Malchiodi, Andrea Mondino
We construct embedded Willmore tori with small area constraint in Riemannian three-manifolds under some curvature condition used to prevent Möbius degeneration. The construction re…
Structure Theory of Metric-Measure Spaces with Lower Ricci Curvature Bounds
Andrea Mondino, Aaron Naber
We prove that a metric measure space satisfying finite dimensional lower Ricci curvature bounds and whose Sobolev space is Hilbert is rectifiable. That is, a $R…
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…
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…