Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.19198 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In this paper we establish higher-order Sobolev and Rellich-type inequalities on non-compact Riemannian manifolds supporting an isoperimetric inequality. We highlight two notable settings: manifolds with non-negative Ricci curvature and having Euclidean volume growth (supporting Brendle's isoperimetric inequality) and manifolds with non-positive sectional curvature (satisfying the Cartan-Hadamard conjecture or supporting Croke's isoperimetric inequality). Our proofs rely on various symmetrization techniques, the key ingredient is an iterated Talenti's comparison principle. The non-iterated version is analogous to the main result of Chen and Li [J. Geom. Anal., 2023].