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Calabi flow in Riemann surfaces revisited: A new point of view

Xiuxiong Chen
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Abstract

In this paper, we observe a set of functionals of metrics which are all decrease under the Calabi flow and have uniform lower bound along the flow, which give rise to a set of integral estimates on the curvature flow. Using these estimates, together with weak compactness we obtained in previous papers [8] and [10], we prove the long term existence and convergence of the Calabi flow. Thus give a new proof to Chruscial's theorem. The set of simple ideas of global integral estimates and concentration compactness should have further implications in other heat flow problems.

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Xiuxiong Chen. 2000-10-04. Calabi flow in Riemann surfaces revisited: A new point of view. https://arxiv.org/abs/math/0009246

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