The Michael-Simon-Sobolev inequality on manifolds for positive symmetric tensor fields

The Michael-Simon-Sobolev inequality on manifolds for positive symmetric tensor fields

We prove the Michael-Simon-Sobolev inequality for smooth symmetric uniformly positive definite (0, 2)-tensor fields on compact submanifolds with or without boundary in Riemannian manifolds with nonnegative sectional curvature by the Alexandrov-Bakelman-Pucci (ABP) method. It should be a generalizati...

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Veröffentlicht in:arXiv.org 2024-09
Hauptverfasser: Wu, Yuting, Chengyang Yi, Zheng, Yu
Format: Artikel
Sprache:eng
Schlagworte:
Manifolds (mathematics)
Riemann manifold
Tensors
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Zusammenfassung:We prove the Michael-Simon-Sobolev inequality for smooth symmetric uniformly positive definite (0, 2)-tensor fields on compact submanifolds with or without boundary in Riemannian manifolds with nonnegative sectional curvature by the Alexandrov-Bakelman-Pucci (ABP) method. It should be a generalization of S. Brendle in [2].
ISSN:2331-8422