Preserving curvature lower bounds when Ricci flowing non-smooth initial data
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912128444661760 |
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| author | Simon, Miles |
| author_facet | Simon, Miles |
| contents | In this paper we survey some results on Ricci flowing non-smooth initial data. Among other things, we give a non-exhaustive list of various weak initial data which can be evolved with the Ricci flow. We also survey results which show that various curvature lower bounds will, possibly up to a constant, be preserved, if we start with such possibly non-smooth initial data. Some proofs/proof sketches are given in certain cases. A list of some open problems related to these areas is given in the last section of the paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13204 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Preserving curvature lower bounds when Ricci flowing non-smooth initial data Simon, Miles Differential Geometry Analysis of PDEs Metric Geometry 53E20 In this paper we survey some results on Ricci flowing non-smooth initial data. Among other things, we give a non-exhaustive list of various weak initial data which can be evolved with the Ricci flow. We also survey results which show that various curvature lower bounds will, possibly up to a constant, be preserved, if we start with such possibly non-smooth initial data. Some proofs/proof sketches are given in certain cases. A list of some open problems related to these areas is given in the last section of the paper. |
| title | Preserving curvature lower bounds when Ricci flowing non-smooth initial data |
| topic | Differential Geometry Analysis of PDEs Metric Geometry 53E20 |
| url | https://arxiv.org/abs/2411.13204 |