All two-dimensional expanding Ricci solitons
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916521006071808 |
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| author | Peachey, Luke T. Topping, Peter M. |
| author_facet | Peachey, Luke T. Topping, Peter M. |
| contents | The second author and H. Yin have developed a Ricci flow existence theory that gives a complete Ricci flow starting with a surface equipped with a conformal structure and a nonatomic Radon measure as a volume measure. This led to the discovery of a large array of new expanding Ricci solitons. In this paper we use the recent uniqueness theory in this context, also developed by the second author and H. Yin, to give a complete classification of all expanding Ricci solitons on surfaces. Along the way, we prove a converse to the existence theory that is not constrained to solitons: every complete Ricci flow on a surface over a time interval $(0,\varepsilon)$ admits a $t\downarrow 0$ limit within the class of admissible initial data. This makes surfaces the first nontrivial setting for Ricci flow in which a bijection can be given between the entire set of complete Ricci flows over maximal time intervals $(0,T)$, and a class of initial data that induces them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05306 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | All two-dimensional expanding Ricci solitons Peachey, Luke T. Topping, Peter M. Differential Geometry 53E20 The second author and H. Yin have developed a Ricci flow existence theory that gives a complete Ricci flow starting with a surface equipped with a conformal structure and a nonatomic Radon measure as a volume measure. This led to the discovery of a large array of new expanding Ricci solitons. In this paper we use the recent uniqueness theory in this context, also developed by the second author and H. Yin, to give a complete classification of all expanding Ricci solitons on surfaces. Along the way, we prove a converse to the existence theory that is not constrained to solitons: every complete Ricci flow on a surface over a time interval $(0,\varepsilon)$ admits a $t\downarrow 0$ limit within the class of admissible initial data. This makes surfaces the first nontrivial setting for Ricci flow in which a bijection can be given between the entire set of complete Ricci flows over maximal time intervals $(0,T)$, and a class of initial data that induces them. |
| title | All two-dimensional expanding Ricci solitons |
| topic | Differential Geometry 53E20 |
| url | https://arxiv.org/abs/2307.05306 |