Higher-order Sobolev and Rellich inequalities via iterated Talenti's principle
Abstract
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, and 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].
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - S
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 28
- Issue
- 0
- Pages
- 139–152
- Publication date
- 1 January 2026