Cohomogeneity two Ricci solitons with sub-Euclidean volume
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911247153233920 |
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| author | Firester, Benjy Tsiamis, Raphael |
| author_facet | Firester, Benjy Tsiamis, Raphael |
| contents | We introduce new families of four-dimensional Ricci solitons of cohomogeneity two with volume collapsing ends. In a local presentation of the metric conformal to a product, we reduce the soliton equation to a degenerate Monge-Ampère equation for the conformal factor coupled with ODEs. We obtain explicit complete expanding solitons as well as abstract existence results for shrinking and steady solitons with boundary. These families of Ricci solitons specialize to classical examples of Einstein and soliton metrics. We also classify local solutions of this Monge-Ampère equation to prove rigidity for these solitons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13982 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomogeneity two Ricci solitons with sub-Euclidean volume Firester, Benjy Tsiamis, Raphael Differential Geometry Analysis of PDEs We introduce new families of four-dimensional Ricci solitons of cohomogeneity two with volume collapsing ends. In a local presentation of the metric conformal to a product, we reduce the soliton equation to a degenerate Monge-Ampère equation for the conformal factor coupled with ODEs. We obtain explicit complete expanding solitons as well as abstract existence results for shrinking and steady solitons with boundary. These families of Ricci solitons specialize to classical examples of Einstein and soliton metrics. We also classify local solutions of this Monge-Ampère equation to prove rigidity for these solitons. |
| title | Cohomogeneity two Ricci solitons with sub-Euclidean volume |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2408.13982 |