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arXiv · 2610.05217

Long-time existence of the Calabi flow on Kähler surfaces with bounded Sobolev constants

Haozhao Li·Bing Wang·Kai Zheng
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Abstract

We prove that the Calabi flow extends past any finite time on compact Kähler surfaces if its Sobolev constants remain uniformly bounded. Moreover, we show the long-time existence of Calabi flow in certain Kähler classes on compact Kähler surfaces when the initial Calabi energy is strictly below an explicit threshold.

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Haozhao Li, Bing Wang, Kai Zheng. 2026-10-04. Long-time existence of the Calabi flow on Kähler surfaces with bounded Sobolev constants. https://arxiv.org/abs/2610.05217

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