课程名称：

1. Title: Three circle theorem on Kahler manifolds and applications

Abstract:
 The classical Hadamard Three Circle theorem is generalized complete Kahler manifolds with nonnegative holomorphic sectional curvature. Various applications will be discussed. For example, the connection with Yau's uniformization conjectures; the resolution of Ni's  conjecture on complete Kahler manifolds with nonnegative bisectional curvature.

2. Title: On the existence of polynomial growth holomorphic functions on complete K/"ahler manifolds with nonnegative bisectional curvature

Abstract:
We give a proof to Lei Ni's conjecture on the existence of polynomial growth holomorphic functions on complete K/"ahler manifolds with nonnegative bisectional curvature. The tools are Gromov-Hausdorff convergence theory and the three circle theorem.

3. Title: Gromov-Hausdorff convergence of K/"ahler manifolds and the finite generation conjecture

Abstract:
We study the uniformization conjecture of Yau by using the Gromov-Haudorff convergence. As a consequence, we confirm Yau's finite generation conjecture. More precisely, on complete noncompact Kahler manifold with nonnegative bisectional curvature, the ring of polynomial growth holomorphic functions is finitely generated.  We also prove that if M is a complete noncompact Kahler manifold with nonnegative bisectional curvature and maximal volume growth, then it is biholomorphic to an affine algebraic variety.

4. Gromov-Hausdorff limits of K/"ahler manifolds with bisectional curvature lower bound

Abstract: Given a sequence of complete(compact or noncompact) K/"ahler manifolds M^n_i with bisectional curvature lower bound and noncollapsed volume, we prove that the pointed Gromov-Hausdorff limit is homeomorphic to a normal complex analytic variety. The complex analytic structure is induced from the limit of M^n_i.

授课人：刘刚教授（加州大学伯克利分校）

时间：6月10日，11日，12日，13日 下午2:00-4:00

地点：管理楼1418