The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature
Chengyang Yi , Yu Zheng
Chinese Annals of Mathematics, Series B ›› 2024, Vol. 45 ›› Issue (3) : 487 -496.
The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature
The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature. This extends a recent result of Brendle with Euclidean setting.
Logarithmic Sobolev inequality / Nonnegative sectional curvature / Submanifold
| [1] |
|
| [2] |
Brendle, S., Sobolev inequalities in manifolds with nonnegative curvature, Communications on Pure and Applied Mathematics, arXiv: 2009.13717v3. |
| [3] |
Brendle, S., Sobolev inequalities in manifolds with nonnegative curvature, Communications on Pure and Applied Mathematics, arXiv: 2009.13717v5. |
| [4] |
Brendle, S., Minimal hypersurfaces and geometric inequalities, Preprint, to appear in Annales de la Faculté des Sciences de Toulouse, arXiv: 2010.03425v2. |
| [5] |
|
| [6] |
|
| [7] |
|
| [8] |
|
| [9] |
|
| [10] |
Chow, B., Lu, P. and Ni, L., Hamilton’s Ricci Flow, AMS Graduate Studies in Mathematics, Providence, RI, 2006. |
| [11] |
Colding, T. H. and Minnicozzi, W. II, A course in minimal surfaces, AMS Graduate Studies in Mathematics, Providence, RI, 2011. |
| [12] |
|
| [13] |
|
| [14] |
|
| [15] |
|
| [16] |
|
| [17] |
|
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