Kähler-Ricci flows coming out of metric spaces
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914161357750272 |
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| author | Deruelle, Alix Guedj, Vincent Guenancia, Henri Zeriahi, Ahmed |
| author_facet | Deruelle, Alix Guedj, Vincent Guenancia, Henri Zeriahi, Ahmed |
| contents | Given a compact Kähler manifold $X$ and a closed, positive $(1,1)$-current $T$ on $X$, we find sufficient conditions for $T$ to induce a metric structure $(X,d_T)$ which is the Gromov-Hausdorff limit of compact Kähler manifolds either in a "static" way or at time zero of smooth Kähler-Ricci flows. In dimension $1$ we extend works of T. Richard and M. Simon, showing that any oriented compact Alexandrov surface with bounded integral curvature and without cusp is the initial datum of a Kähler-Ricci flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kähler-Ricci flows coming out of metric spaces Deruelle, Alix Guedj, Vincent Guenancia, Henri Zeriahi, Ahmed Differential Geometry Analysis of PDEs 53E30, 32W20, 35K55 Given a compact Kähler manifold $X$ and a closed, positive $(1,1)$-current $T$ on $X$, we find sufficient conditions for $T$ to induce a metric structure $(X,d_T)$ which is the Gromov-Hausdorff limit of compact Kähler manifolds either in a "static" way or at time zero of smooth Kähler-Ricci flows. In dimension $1$ we extend works of T. Richard and M. Simon, showing that any oriented compact Alexandrov surface with bounded integral curvature and without cusp is the initial datum of a Kähler-Ricci flow. |
| title | Kähler-Ricci flows coming out of metric spaces |
| topic | Differential Geometry Analysis of PDEs 53E30, 32W20, 35K55 |
| url | https://arxiv.org/abs/2511.13473 |