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

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.

arXiv comment34 pages