Abstract
We study the line bundle mean curvature flow on Kähler surfaces under the hypercritical phase and a certain semipositivity condition. We naturally encounter such a condition when considering the blowup of Kähler 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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Notes
In [14], they made an assumption that the form F arises as curvature of a fiber metric on a holomorphic line bundle. But this assumption is only for aesthetic purposes and not essentially used in their paper.
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Communicated by P. Topping.
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