Abstract:A complex manifold is called an Oka manifold if continuous maps from Stein manifolds can be deformed into holomorphic maps with approximation and interpolation. Oka manifolds are characterized by a certain kind of ellipticity which is the opposite of Kobayashi-Eisenman-Brody hyperbolicity. Based on the fact that the zero section of a negative line bundle on a compact complex manifold ...
AbstractThe 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...