Higher-order Sobolev and Rellich inequalities via iterated Talenti's principle
Analysis of PDEs
2026-01-13 v2
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, 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].
Keywords
Cite
@article{arxiv.2509.19198,
title = {Higher-order Sobolev and Rellich inequalities via iterated Talenti's principle},
author = {Csaba Farkas and Sándor Kajántó},
journal= {arXiv preprint arXiv:2509.19198},
year = {2026}
}