Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

G Antonelli, E Pasqualetto, M Pozzetta… - Mathematische …, 2024 - Springer
This paper studies sharp and rigid isoperimetric comparison theorems and asymptotic
isoperimetric properties for small and large volumes on N-dimensional RCD (K, N) spaces …

Isoperimetry on manifolds with ricci bounded below: overview of recent results and methods

M Pozzetta - … : Anisotropic Isoperimetric Problems & Related Topics, 2022 - Springer
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 …

Isoperimetric problem and structure at infinity on Alexandrov spaces with nonnegative curvature

G Antonelli, M Pozzetta - arxiv preprint arxiv:2302.10091, 2023 - arxiv.org
In this paper we consider nonnegatively curved finite dimensional Alexandrov spaces such
that unit balls have volumes uniformly bounded from below away from zero. We study the …

Second-order estimates for the -Laplacian in RCD spaces

L Benatti, IY Violo - arxiv preprint arxiv:2401.09982, 2024 - arxiv.org
We establish quantitative second-order Sobolev regularity for functions having a $2 $-
integrable $ p $-Laplacian in bounded RCD spaces, with $ p $ in a suitable range. In the …

Rigidity of mean convex subsets in non-negatively curved RCD spaces and stability of mean curvature bounds

C Ketterer - Journal of Topology and Analysis, 2023 - World Scientific
We prove splitting theorems for mean convex open subsets in Riemannian curvature-
dimension (RCD) spaces that extend results by Kasue et al. for Riemannian manifolds with …

On the topology of manifolds with nonnegative Ricci curvature and linear volume growth

D Navarro, J Pan, X Zhu - arxiv preprint arxiv:2410.15488, 2024 - arxiv.org
Understanding the relationships between geometry and topology is a central theme in
Riemannian geometry. We establish two results on the fundamental groups of open …

Isoperimetry on Manifolds with Ricci

M Pozzetta - Anisotropic Isoperimetric Problems and Related …, 2024 - books.google.com
We review recent results on the study of the isoperimetric problem on Rie-mannian
manifolds with Ricci lower bounds. We focus on the validity of sharp second order …

Ricci curvature bounded below and uniform rectifiability

M Hyde, M Villa, IY Violo - arxiv preprint arxiv:2311.09907, 2023 - arxiv.org
arxiv:2311.09907v1 [math.MG] 16 Nov 2023 Page 1 arxiv:2311.09907v1 [math.MG] 16 Nov
2023 RICCI CURVATURE BOUNDED BELOW AND UNIFORM RECTIFIABILITY MATTHEW …