Sobolev Inequalities in Manifolds with Nonnegative Curvature |
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Authors: | Simon Brendle |
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Institution: | Columbia University, 2990 Broadway, New York, NY, 10027 USA |
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Abstract: | 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. |
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