Ricci flow from spaces with edge type conical singularities
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866918087919403008 |
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| author | Lavoyer, Lucas |
| author_facet | Lavoyer, Lucas |
| contents | We study the Ricci flow out of spaces with edge type conical singularities along a closed, embedded curve. Under the additional assumption that for each point of the curve, our space is locally modelled on the product of a fixed positively curved cone and a line, we show existence of a solution to Ricci flow $(M,g(t))$ for $t\in (0,T],$ which converges back to the singular space as $t\searrow 0$ in the pointed Gromov-Hausdorff topology. We also prove curvature estimates for the solution and, for edge points, we show that the tangent flow at these points is a positively curved expanding Ricci soliton solution crossed with a line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00344 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ricci flow from spaces with edge type conical singularities Lavoyer, Lucas Differential Geometry Analysis of PDEs We study the Ricci flow out of spaces with edge type conical singularities along a closed, embedded curve. Under the additional assumption that for each point of the curve, our space is locally modelled on the product of a fixed positively curved cone and a line, we show existence of a solution to Ricci flow $(M,g(t))$ for $t\in (0,T],$ which converges back to the singular space as $t\searrow 0$ in the pointed Gromov-Hausdorff topology. We also prove curvature estimates for the solution and, for edge points, we show that the tangent flow at these points is a positively curved expanding Ricci soliton solution crossed with a line. |
| title | Ricci flow from spaces with edge type conical singularities |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2305.00344 |