Surveys in Differential Geometry

Volume 26 (2021)

A survey on Yau’s uniformization conjecture

Pages: 13 – 30

DOI: https://dx.doi.org/10.4310/SDG.2021.v26.n1.a2

Authors

Bing-Long Chen (Department of Mathematics, Sun Yat-sen University, Guangzhou, China)

Xi-Ping Zhu (Department of Mathematics, Sun Yat-sen University, Guangzhou, China)

Abstract

This is a survey on Yau’s uniformization conjecture which states that any complete noncompact Kähler manifold with positive holomorphic bisectional curvature is biholomorphic to $\mathbb{C}^n$. The accomplishments of the conjecture during the past decades and recent developments, from the view point of geometry, will be reviewed.

Keywords

uniformization conjecture, non-maximal volume growth, Chern number

2010 Mathematics Subject Classification

53C25, 53C44

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This work is partially supported by National Key R&D Program of China 2022 YFA1005400 and NSFC12141106, 12271530.

Published 22 January 2024