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Sobolev Inequality In Manifolds With Lower Quadratic Curvature Decay

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arxiv 2503.19254 v1 pith:NIG6WBH7 submitted 2025-03-25 math.DG

Tian Chong , Han Luo , Lingen Lu This is my paper · ORCID
classification math.DG
keywords curvaturedecaylowerquadraticsobolevbrendlecabrcompact
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By using the ABP method developed by Cabr\'e and Brendle, we establish some Sobolev inequalities for compact domains and submanifolds in a complete Riemannian manifold with lower quadratic curvature decay

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  1. Fenchel-Willmore-Chen inequality under lower bounds on weighted intermediate Ricci curvature

    math.DG 2026-08 conditional novelty 7.0 of 10

    The paper proves a Fenchel-Willmore-Chen inequality for submanifolds in smooth metric measure spaces with lower bounds on the 1-Bakry-Emery n-Ricci curvature, plus Sobolev and isoperimetric inequalities under nonnegat...

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