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Convergence of the J-flow on Kahler surfaces

Ben Weinkove
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Abstract

Donaldson defined a parabolic flow on Kahler manifolds which arises from considering the action of a group of symplectomorphisms on the space of smooth maps between manifolds. One can define a moment map for this action, and then consider the gradient flow of the square of its norm. Chen discovered the same flow from a different viewpoint and called it the J-flow, since it corresponds to the gradient flow of his J-functional, which is related to Mabuchi's K-energy. In this paper, we show that in the case of Kahler surfaces with two Kahler forms satisfying a certain inequality, the J-flow converges to a zero of the moment map.

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Ben Weinkove. 2004-10-19. Convergence of the J-flow on Kahler surfaces. https://arxiv.org/abs/math/0306012

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