Smoothing a measure on a Riemann surface using Ricci flow
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866910751543787520 |
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| author | Topping, Peter M. Yin, Hao |
| author_facet | Topping, Peter M. Yin, Hao |
| contents | We formulate and solve the existence problem for Ricci flow on a Riemann surface with initial data given by a Radon measure as volume measure. The theory leads us to a large class of new examples of nongradient expanding Ricci solitons, including the first example of a nongradient Kaehler Ricci soliton. It also settles the question of whether a smooth flow for positive time that attains smooth initial data in a distance metric sense must be smooth down to the initial time. We disprove this by giving an example of a complete Ricci flow starting with the Euclidean plane that is not the static solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_14686 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Smoothing a measure on a Riemann surface using Ricci flow Topping, Peter M. Yin, Hao Differential Geometry Analysis of PDEs 53E20 We formulate and solve the existence problem for Ricci flow on a Riemann surface with initial data given by a Radon measure as volume measure. The theory leads us to a large class of new examples of nongradient expanding Ricci solitons, including the first example of a nongradient Kaehler Ricci soliton. It also settles the question of whether a smooth flow for positive time that attains smooth initial data in a distance metric sense must be smooth down to the initial time. We disprove this by giving an example of a complete Ricci flow starting with the Euclidean plane that is not the static solution. |
| title | Smoothing a measure on a Riemann surface using Ricci flow |
| topic | Differential Geometry Analysis of PDEs 53E20 |
| url | https://arxiv.org/abs/2107.14686 |