Collapsing of the line bundle mean curvature flow on Kähler surfaces

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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.

Original languageEnglish
Article number27
JournalCalculus of Variations and Partial Differential Equations
Volume60
Issue number1
DOIs
Publication statusPublished - Feb 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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