STABILITY OF LINE BUNDLE MEAN CURVATURE FLOW

Let (X, & omega;) be a compact Ka & BULL;hler manifold of complex dimension n and (L, h) be a holomorphic line bundle over X. The line bundle mean curvature flow was introduced by Jacob-Yau 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<SIC> on L. We prove that the line bundle mean curvature flow converges to h<SIC> exponentially in C & INFIN; sense as long as the initial metric is close to h<SIC> in C2-norm.