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 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.

Time: 10:10am-12:00pm, Tuesday, June 23

Place: Room 29, Quan Zhai, BICMR

Speaker: LIU Gang, Berkeley