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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.12381 |
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| _version_ | 1866916846645542912 |
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| author | Cunha, Antonio W. Silva Jr, Antonio N. Wylie, William |
| author_facet | Cunha, Antonio W. Silva Jr, Antonio N. Wylie, William |
| contents | In this work, we study gradient solitons to general geometric flows. Our approach is to understand what assumptions need to be made about a flow in order to extend results about Ricci solitons. In this direction, we identify an identity, first exploited in the pioneering work of Richard Hamilton in the case of Ricci solitons, which we call Hamilton's identity. We show that a version of this identity for an arbitrary geometric flow allows one to recover results about rigidity, the growth of the potential function, volume growth and the Omori-Yau maximum principle that have been proven for gradient Ricci solitons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamilton's identity and rigidity of complete gradient solitons Cunha, Antonio W. Silva Jr, Antonio N. Wylie, William Differential Geometry 53C24 In this work, we study gradient solitons to general geometric flows. Our approach is to understand what assumptions need to be made about a flow in order to extend results about Ricci solitons. In this direction, we identify an identity, first exploited in the pioneering work of Richard Hamilton in the case of Ricci solitons, which we call Hamilton's identity. We show that a version of this identity for an arbitrary geometric flow allows one to recover results about rigidity, the growth of the potential function, volume growth and the Omori-Yau maximum principle that have been proven for gradient Ricci solitons. |
| title | Hamilton's identity and rigidity of complete gradient solitons |
| topic | Differential Geometry 53C24 |
| url | https://arxiv.org/abs/2507.12381 |