Sobolev Inequalities in Manifolds with Nonnegative Curvature

By S. Brendle. Communications on Pure and Applied Mathematics, 2020

94 citations recorded by the source corpus.

We prove a sharp Sobolev inequality on manifolds with nonnegative Ricci curvature. Moreover, we prove a Michael‐Simon inequality for submanifolds in manifolds with nonnegative sectional curvature. Both inequalities depend on the asymptotic volume ratio of the ambient manifold. © 2022 Wiley Periodicals LLC.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c80f511369da4602f9a6f1790940595395094474

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In Applied Mathematics

1. Zoltán M. Balogh
2. Daniele Semola
3. Enrico Pasqualetto
4. G. Antonelli
5. Alexandru Krist'aly
6. Marco Pozzetta
7. G. Lu
8. Francesco Serra Cassano

In Mathematical Physics

1. Zoltán M. Balogh
2. Daniele Semola
3. Enrico Pasqualetto
4. G. Antonelli
5. Alexandru Krist'aly
6. Marco Pozzetta

Citations in the corpus

• Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature (2020, methodology): “4 The smoothness of the boundary of the isoperimetric set is an essential requirement not only in our argument, but also inAgostiniani, Fogagnolo andMazzieri [1, 25] and Brendle [7].”
• Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds (2022, methodology): “The approach presented is suited for dealing with the rigidity case, thus extending the rigidity result for the sharp isoperimetric inequality treated in [22, 17, 1, 45].”