Gap theorem on Kähler manifolds with nonnegative orthogonal bisectional curvature
-
Lei Ni
and
Yanyan Niu
Abstract
In this paper we prove a gap theorem for Kähler manifolds with nonnegative orthogonal bisectional curvature and nonnegative Ricci curvature, which generalizes an earlier result of the first author [L. Ni, An optimal gap theorem, Invent. Math. 189 2012, 3, 737–761]. We also prove a Liouville theorem for plurisubharmonic functions on such a manifold, which generalizes a previous result of L.-F. Tam and the first author [L. Ni and L.-F. Tam, Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature, J. Differential Geom. 64 2003, 3, 457–524] and complements a recent result of Liu [G. Liu, Three-circle theorem and dimension estimate for holomorphic functions on Kähler manifolds, Duke Math. J. 165 2016, 15, 2899–2919].
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1401500
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: NSFC-11301354
Award Identifier / Grant number: NSFC-11571260
Funding statement: The research of the first author is partially supported by National Science Foundation grant DMS-1401500 and the “Capacity Building for Sci-Tech Innovation-Fundamental Research Funds”. The research of the second author is partially supported by National Natural Science Foundation of China grant NSFC-11301354, NSFC-11571260, and by Youth Innovation Research Team of Capital Normal University.
Acknowledgements
We would like to thank Professor Luen-Fei Tam for suggesting the problem of the gap theorem for manifolds with nonnegative orthogonal bisectional curvature.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- When the sieve works II
- A gluing approach for the fractional Yamabe problem with isolated singularities
- Dehn functions and Hölder extensions in asymptotic cones
- Gap theorem on Kähler manifolds with nonnegative orthogonal bisectional curvature
- Kähler geometry of horosymmetric varieties, and application to Mabuchi’s K-energy functional
- Asymptotics for the level set equation near a maximum
- Construction of constant mean curvature n-noids using the DPW method
- Irreducible components of the eigencurve of finite degree are finite over the weight space
- Structure theorems for singular minimal laminations
Articles in the same Issue
- Frontmatter
- When the sieve works II
- A gluing approach for the fractional Yamabe problem with isolated singularities
- Dehn functions and Hölder extensions in asymptotic cones
- Gap theorem on Kähler manifolds with nonnegative orthogonal bisectional curvature
- Kähler geometry of horosymmetric varieties, and application to Mabuchi’s K-energy functional
- Asymptotics for the level set equation near a maximum
- Construction of constant mean curvature n-noids using the DPW method
- Irreducible components of the eigencurve of finite degree are finite over the weight space
- Structure theorems for singular minimal laminations
