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arXiv · 2509.19198

Higher-order Sobolev and Rellich inequalities via iterated Talenti's principle

Csaba Farkas·Sándor Kajántó
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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].

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Csaba Farkas, Sándor Kajántó. 2025-09-23. Higher-order Sobolev and Rellich inequalities via iterated Talenti's principle. https://arxiv.org/abs/2509.19198

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