Gromov-Hausdorff limits of Kähler manifolds and the finite generation conjecture

Gang Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We study the uniformization conjecture of Yau by using the Gromov-Hausdorff 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. During the course of the proof, we prove if Mn is a complete noncompact Kähler manifold with nonnegative bisectional curvature and maximal volume growth, then M is biholomorphic to an affine algebraic variety. We also confirm a conjecture of Ni on the existence of polynomial growth holomorphic functions on Kähler manifolds with nonnegative bisectional curvature.

Original languageEnglish (US)
Pages (from-to)775-815
Number of pages41
JournalAnnals of Mathematics
Volume184
Issue number3
DOIs
StatePublished - 2016

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint

Dive into the research topics of 'Gromov-Hausdorff limits of Kähler manifolds and the finite generation conjecture'. Together they form a unique fingerprint.

Cite this