Equidistribution of inverse images of analytic subsets for holomorphic endomorphisms of compact Kaehler manifolds

초록

In this talk, we discuss the limit of inverse images of analytic subsets under a given holomorphic endomorphism of a compact K\"ahler manifold. We expect that the limit should be inside the Julia set of the given map in a reasonable sense under reasonable conditions. We will study a sufficient condition with emphasis on the difference between the complex projective space and a general compact K\"ahler manifold. In particular, we introduce the regularization of a positive closed currents with quantitative estimates and some estimates related to semi-regular transforms of currents, which are closely related to superpotentials.