EVENT DETAILS AND ABSTRACT

Title: Gromov-Hausdorff convergence of Kähler manifolds and the finite generation conjecture
Speaker: Gang Liu
Speaker Info: Berkeley
Brief Description:
Special Note:
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 a complete noncompact Kähler manifold with nonnegative bisectional curvature, the ring of polynomial growth holomorphic functions is finitely generated. We prove if M is a complete noncompact Kähler manifold with nonnegative bisectional curvature and maximal volume growth, then it is biholomorphic to an affine algebraic variety. We also confirm a conjecture of Ni on the existence of polynomial growth holomorphic functions on complete Kähler manifolds with nonnegative bisectional curvature.