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arXiv · 2611.01882

Convergence of the Calabi flow on Kähler surfaces with bounded Sobolev constants

Haozhao Li·Bing Wang·Kai Zheng
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Abstract

We study global Calabi flows $g(t)$ on compact Kähler surfaces with a uniform Sobolev constant. For any sequence $t_j\to\infty$, set $g_j(t):=g(t_j+t)$. After passing to a subsequence, these flows converge to an eternal Calabi flow on a compact extremal Kähler orbifold surface. The convergence holds in the spacetime $\hat C^\infty$-Cheeger--Gromov topology: it is uniform in the Gromov--Hausdorff sense on compact time intervals and smooth away from the orbifold singularities, using comparisons fixed in time.

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Haozhao Li, Bing Wang, Kai Zheng. 2026-11-01. Convergence of the Calabi flow on Kähler surfaces with bounded Sobolev constants. https://arxiv.org/abs/2611.01882

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