Abstract

The line bundle mean curvature flow was defined by A. Jacob and S.-T. Yau to obtain a deformed Hermitian Yang-Mills metric on a line bundle over a Kahler manifold. In this talk, I would like to explain an epsilon regularity theorem for the line bundle mean curvature flow. This is joint work with Xiaoli Han. To explain the outline of the proof, I would like to introduce a scale-invariant monotone quantity, a notion of self-shrinkers and the Liouville type theorem for those self-shrinkers.