Geometric inequalities and rigidity of gradient shrinking Ricci solitons
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866910787177545728 |
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| author | Wu, Jia-Yong |
| author_facet | Wu, Jia-Yong |
| contents | In this paper we prove that the Sobolev inequality, the logarithmic Sobolev inequality, the Schrödinger heat kernel upper bound, the Faber-Krahn inequality, the Nash inequality and the Rozenblum-Cwikel-Lieb inequality all equivalently exist on complete gradient shrinking Ricci solitons. We also obtain some integral gap theorems for compact shrinking Ricci solitons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_12725 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Geometric inequalities and rigidity of gradient shrinking Ricci solitons Wu, Jia-Yong Differential Geometry Analysis of PDEs 53C25, 53C20, 53C24, 58J35 In this paper we prove that the Sobolev inequality, the logarithmic Sobolev inequality, the Schrödinger heat kernel upper bound, the Faber-Krahn inequality, the Nash inequality and the Rozenblum-Cwikel-Lieb inequality all equivalently exist on complete gradient shrinking Ricci solitons. We also obtain some integral gap theorems for compact shrinking Ricci solitons. |
| title | Geometric inequalities and rigidity of gradient shrinking Ricci solitons |
| topic | Differential Geometry Analysis of PDEs 53C25, 53C20, 53C24, 58J35 |
| url | https://arxiv.org/abs/2009.12725 |