Stability of line bundle mean curvature flow

Abstract

Let $(X,\omega )$ 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 \cite{JY} 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 $\hat{h}$ on $L$. We prove that the line bundle mean curvature flow converges to $\hat{h}$ exponentially in $C^{\infty }$ sense as long as the initial metric is close to $\hat{h}$ in $C^2$-norm.

Minor corrections in the proof of Theorem 1.5 on pp 22