On weak formulations of (super) Ricci flows
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913022386110464 |
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| author | Lakzian, Sajjad |
| author_facet | Lakzian, Sajjad |
| contents | We present two characterizations of smooth compact Ricci flow solutions solely in terms of metrics and measures (one of them only works under positive scalar curvature along the flow); thus, provide weak formulations that are generalized to the singular setting in a straightforward manner. These formulations are achieved by weakly formulating super Ricci flows and imposing a saturation condition (solely in terms of metric and measure) to ensure the super Ricci flow inequality is an equality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10007 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On weak formulations of (super) Ricci flows Lakzian, Sajjad Differential Geometry Analysis of PDEs Functional Analysis Metric Geometry 53E20, 53C21, 53C23, 49Q22 We present two characterizations of smooth compact Ricci flow solutions solely in terms of metrics and measures (one of them only works under positive scalar curvature along the flow); thus, provide weak formulations that are generalized to the singular setting in a straightforward manner. These formulations are achieved by weakly formulating super Ricci flows and imposing a saturation condition (solely in terms of metric and measure) to ensure the super Ricci flow inequality is an equality. |
| title | On weak formulations of (super) Ricci flows |
| topic | Differential Geometry Analysis of PDEs Functional Analysis Metric Geometry 53E20, 53C21, 53C23, 49Q22 |
| url | https://arxiv.org/abs/2604.10007 |