# Gromov-Haudorff convergence of Kahler manifolds and the finite generation conjecture

Friday, February 13, 2015 -

3:00pm to 4:00pm

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 Kahler manifold ith nonnegative bisectional curvature, the ring of polynomial growth holomorphic functions is finitely generated. During the course, we prove 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. We also confirm a conjecture of Ni on the equivalence of several conditions on complete Kahler manifolds with nonnegative bisectional curvature.

Speaker:

Gang Liu

U.C. Berkeley

Event Location:

Fine Hall 314