The rigidity of eigenfunctions' gradient estimates
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916540881829888 |
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| author | Xu, Guoyi Xue, Xiaolong |
| author_facet | Xu, Guoyi Xue, Xiaolong |
| contents | On compact Riemannian manifolds with non-negative Ricci curvature and smooth (possibly empty), convex (or mean convex) boundary, if the sharp Li-Yau type gradient estimate of an Neumann (or Dirichlet) eigenfunction holds at some non-critical points of the eigenfunction; we show that the manifold is isometric to the product of one lower dimension manifold and a round circle (or a line segment). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05517 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The rigidity of eigenfunctions' gradient estimates Xu, Guoyi Xue, Xiaolong Differential Geometry Analysis of PDEs Spectral Theory On compact Riemannian manifolds with non-negative Ricci curvature and smooth (possibly empty), convex (or mean convex) boundary, if the sharp Li-Yau type gradient estimate of an Neumann (or Dirichlet) eigenfunction holds at some non-critical points of the eigenfunction; we show that the manifold is isometric to the product of one lower dimension manifold and a round circle (or a line segment). |
| title | The rigidity of eigenfunctions' gradient estimates |
| topic | Differential Geometry Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2405.05517 |