32 citations · 126 across the 14 of their papers we have counts for
14 papers
Quantitative isoperimetric inequalities in capillarity problems and cones in strong and barycentric forms
Davide Carazzato, Giulio Pascale, Marco Pozzetta
We study quantitative isoperimetric inequalities for two different perimeter-type functionals. We first consider classical capillarity functionals, which measure the perimeter of s…
A sharp spectral splitting theorem
Gioacchino Antonelli, Marco Pozzetta, Kai Xu
We prove a sharp spectral generalization of the Cheeger--Gromoll splitting theorem. We show that if a complete non-compact Riemannian manifold of dimension has at lea…
Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature
Gioacchino Antonelli, Marco Pozzetta, Daniele Semola
Let be a complete Riemannian manifold which is not isometric to , has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature…
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…
Quantitative isoperimetric inequalities for classical capillarity problems
Giulio Pascale, Marco Pozzetta
We consider capillarity functionals which measure the perimeter of sets contained in a Euclidean half-space assigning a constant weight to the portion of the boundary…
Isoperimetry on manifolds with Ricci bounded below: overview of recent results and methods
Marco Pozzetta
We review recent results on the study of the isoperimetric problem on Riemannian manifolds with Ricci lower bounds. We focus on the validity of sharp second order differential ineq…
Topological regularity of isoperimetric sets in PI spaces having a deformation property
Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta +1
We prove topological regularity results for isoperimetric sets in PI spaces having a suitable deformation property, which prescribes a control on the increment of the perimeter of…
Isoperimetric problem and structure at infinity on Alexandrov spaces with nonnegative curvature
Gioacchino Antonelli, Marco Pozzetta
In this paper we consider nonnegatively curved finite dimensional Alexandrov spaces with a non-collapsing condition, i.e., such that unit balls have volumes uniformly bounded from…
Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds
Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta +1
This paper studies sharp and rigid isoperimetric comparison theorems and asymptotic isoperimetric properties for small and large volumes on -dimensional spaces…
The isoperimetric problem via direct method in noncompact metric measure spaces with lower Ricci bounds
Gioacchino Antonelli, Stefano Nardulli, Marco Pozzetta
We establish a structure theorem for minimizing sequences for the isoperimetric problem on noncompact spaces . Under the sole (nec…
Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds
Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta +1
This paper studies sharp isoperimetric comparison theorems and sharp dimensional concavity properties of the isoperimetric profile for non smooth spaces with lower Ricci curvature…
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…
Isoperimetric sets in spaces with lower bounds on the Ricci curvature
Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta
In this paper we study regularity and topological properties of volume constrained minimizers of quasi-perimeters in spaces where the reference measure is the Hausdorff m…
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…