Preservation of product structures under the Ricci flow with instantaneous curvature bounds
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909471404457984 |
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| author | Cook, Mary |
| author_facet | Cook, Mary |
| contents | In this note, we prove that there exists a constant $ε>0$, depending only on the dimension, such that if a complete solution to the Ricci flow splits as a product at time $t=0$ and has curvature bounded by $\fracε{t}$, then the solution splits for all time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_04740 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Preservation of product structures under the Ricci flow with instantaneous curvature bounds Cook, Mary Differential Geometry In this note, we prove that there exists a constant $ε>0$, depending only on the dimension, such that if a complete solution to the Ricci flow splits as a product at time $t=0$ and has curvature bounded by $\fracε{t}$, then the solution splits for all time. |
| title | Preservation of product structures under the Ricci flow with instantaneous curvature bounds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2202.04740 |