30 citations · 47 across the 18 of their papers we have counts for
17 papers · 1 filter
Mean-convex horizontal mean curvature flow in the Heisenberg group
Gaia Bombardieri, Mattia Fogagnolo, Valentina Franceschi
We study the arrival time equation of the mean-convex horizontal mean curvature flow in the Heisenberg group. We prove existence of viscosity solutions when the initial set is hori…
An isoperimetric characterization of a new ADM-like mass for -asymptotically flat manifolds
Luca Benatti, Mattia Fogagnolo
We prove that the notion of mass recently introduced by Mazurowski and Yao for continuous metrics coincides with Huisken's isoperimetric mass on smooth Riemannian -manifolds wit…
Scalar curvature bounds for 3D continuous metrics through the Inverse Mean Curvature Flow
Mattia Fogagnolo, Giorgio Gatti, Alessandra Pluda
We propose a notion of scalar curvature lower bounds in a three-dimensional Riemannian manifold endowed with a metric based on the monotonicity of the Hawking mass along the…
Unexpected phenomena for mean curvature functionals in the Heisenberg group
Mattia Fogagnolo, Andrea Pinamonti, Simone Verzellesi
The Euclidean paradigm that spheres optimize mean curvature variational problems breaks down in the sub-Riemannian Heisenberg group: neither the Pansu sphere nor the Korányi sphere…
Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature
Gioacchino Antonelli, Mattia Fogagnolo, Stefano Nardulli +1
This paper deals with quasi-local isoperimetric versions of the positive mass theorem on -manifolds endowed with continuous complete metrics having nonnegative scalar curvature…
Comparison geometry for substatic manifolds and a weighted Isoperimetric Inequality
Stefano Borghini, Mattia Fogagnolo
Substatic Riemannian manifolds with minimal boundary arise naturally in General Relativity as spatial slices of static spacetimes satisfying the Null Energy Condition. Moreover, th…
The equality case in the substatic Heintze-Karcher inequality
Stefano Borghini, Mattia Fogagnolo, Andrea Pinamonti
We provide a rigidity statement for the equality case for the Heintze-Karcher inequality in substatic manifolds. We apply such result in the warped product setting to fully remove…
Isoperimetric sets in nonnegative scalar curvature and their role through various concepts of mass
Luca Benatti, Mattia Fogagnolo
We review some recent results about the relations among isoperimetric sets, Penrose inequalities and related concepts in the analysis of -manifolds of nonnegative scalar curvatu…
Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature
Luca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri
We deal with suitable nonlinear versions of Jauregui's isocapacitary mass in 3-manifolds with nonnegative scalar curvature and compact outermost minimal boundary. These masses, whi…
On the Isoperimetric Riemannian Penrose Inequality
Luca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri
We prove that the Riemannian Penrose Inequality holds for Asymptotically Flat -manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal d…
The asymptotic behaviour of -capacitary potentials in Asymptotically Conical manifolds
Luca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri
We study the asymptotic behaviour of the -capacitary potential and of the weak Inverse Mean Curvature Flow of a bounded set along the ends of an Asymptotically Conical Riemannia…
On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth
Gioacchino Antonelli, Elia Bruè, Mattia Fogagnolo +1
In this paper we provide new existence results for isoperimetric sets of large volume in Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth. We find…
New Integral Estimates in Substatic Riemannian Manifolds and the Alexandrov Theorem
Mattia Fogagnolo, Andrea Pinamonti
We derive new integral estimates on substatic manifolds with boundary of horizon type, naturally arising in General Relativity. In particular, we generalize to this setting an iden…
The isoperimetric problem on Riemannian manifolds via Gromov-Hausdorff asymptotic analysis
Gioacchino Antonelli, Mattia Fogagnolo, Marco Pozzetta
In this paper we prove the existence of isoperimetric regions of any volume in Riemannian manifolds with Ricci bounded below assuming Gromov--Hausdorff asymptoticity to the suitabl…
Minkowski Inequality on complete Riemannian manifolds with nonnegative Ricci curvature
Luca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri
In this paper we consider Riemannian manifolds of dimension at least , with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth bo…
Minimising hulls, p-capacity and isoperimetric inequality on complete Riemannian manifolds
Mattia Fogagnolo, Lorenzo Mazzieri
The notion of strictly outward minimising hull is investigated for open sets of finite perimeter sitting inside a complete noncompact Riemannian manifold. Under natural geometric a…
Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature
Virginia Agostiniani, Mattia Fogagnolo, Lorenzo Mazzieri
In this paper we consider complete noncompact Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth, of dimension . We prove a sharp…