Stability of line bundle mean curvature flow

2020/01/21 by Xiaoli Han, Han, Xiaoli, Xishen Jin +1 · 1 citation
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2001.07406

Abstract

Let (X,ω) be a compact Kähler manifold of complex dimension n and (L,h) be a holomorphic line bundle over X. The line bundle mean curvature flow was introduced in \citeJY in order to find deformed Hermitian-Yang-Mills metrics on L. In this paper, we consider the stability of the line bundle mean curvature flow. Suppose there exists a deformed Hermitian Yang-Mills metric h on L. We prove that the line bundle mean curvature flow converges to h exponentially in C^∞ sense as long as the initial metric is close to h in C²-norm.

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• The Critical LYZ equation in Kähler Geometry

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