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.

中文翻译：

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线束的塌陷意味着在Kähler曲面上的平均曲率流

我们研究了在超临界相和一定半正性条件下在Kähler表面上的线束平均曲率流。考虑到Kähler曲面的爆炸，我们自然会遇到这种情况。我们表明，该流动平稳地收敛到变形的Hermitian-Yang-Mills方程的奇异解，而远离表面上有限数量的负自相交曲线。作为应用，我们在满足超临界相条件的势函数空间上获得了Kempf-Ness型泛函的下界。