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. 
Gang Liu
U.C. Berkeley
Event Location: 
Fine Hall 314