Collapsing of the line bundle mean curvature flow on K\"ahler surfaces

Ryosuke Takahashi

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arXiv · 1912.13145

Collapsing of the line bundle mean curvature flow on K\"ahler surfaces

Ryosuke Takahashi

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Abstract

We study the line bundle mean curvature flow on K\"ahler surfaces under the hypercritical phase and a certain semipositivity condition. We naturally encounter such a condition when considering the blowup of K\"ahler surfaces. We show that the flow converges smoothly to a singular solution to the deformed Hermitian-Yang-Mills equation away from a finite number of curves of negative self-intersection on the surface. As an application, we obtain a lower bound of a Kempf-Ness type functional on the space of potential functions satisfying the hypercritical phase condition.

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Ryosuke Takahashi. 2019-12-31. Collapsing of the line bundle mean curvature flow on K\"ahler surfaces. https://arxiv.org/abs/1912.13145

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