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arXiv · 2511.13473

K\"ahler-Ricci flows coming out of metric spaces

Alix Deruelle·Vincent Guedj·Henri Guenancia·Ahmed Zeriahi
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Abstract

Given a compact K\"ahler 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 K\"ahler manifolds either in a "static" way or at time zero of smooth K\"ahler-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 K\"ahler-Ricci flow.

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Alix Deruelle, Vincent Guedj, Henri Guenancia, Ahmed Zeriahi. 2025-11-17. K\"ahler-Ricci flows coming out of metric spaces. https://arxiv.org/abs/2511.13473

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