scholarly journals Plurisubharmonic Functions and the Structure of Complete Kähler Manifolds with Nonnegative Curvature

2003 ◽  
Vol 64 (3) ◽  
pp. 457-524 ◽  
Author(s):  
Lei Ni ◽  
Luen-Fai Tam
Keyword(s):  
Nonnegative Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Plurisubharmonic Functions

Gap theorem on Kähler manifolds with nonnegative orthogonal bisectional curvature

2020 ◽  
Vol 2020 (763) ◽  
pp. 111-127 ◽  
Author(s):  
Lei Ni ◽  
Yanyan Niu
Keyword(s):  
Liouville Theorem ◽  
Holomorphic Functions ◽  
Nonnegative Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Nonnegative Ricci Curvature ◽  
Bisectional Curvature ◽  
Plurisubharmonic Functions ◽  
Dimension Estimate ◽  
Gap Theorem

AbstractIn 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].

scholarly journals Kähler manifolds with almost nonnegative curvature

2021 ◽  
Vol 25 (4) ◽  
pp. 1979-2015
Author(s):  
Man-Chun Lee ◽  
Luen-Fai Tam
Keyword(s):  
Nonnegative Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds

scholarly journals The General Definition of the Complex Monge–Ampère Operator on Compact Kähler Manifolds

2010 ◽  
Vol 62 (1) ◽  
pp. 218-239 ◽  
Author(s):  
Yang Xing
Keyword(s):  
Convergence Theorem ◽  
Convex Cone ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
General Definition ◽  
Kahler Manifolds ◽  
Plurisubharmonic Functions ◽  
Definition Of ◽  
Compact Kähler Manifold ◽  
Monge Ampere

AbstractWe introduce a wide subclass of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well defined and the convergence theorem is valid. We also prove that is a convex cone and includes all quasi-plurisubharmonic functions that are in the Cegrell class.

Holomorphic Functions on a Class of Kähler Manifolds With Nonnegative Curvature, I

2020 ◽  
Author(s):  
Bo Yang
Keyword(s):  
Asymptotic Behavior ◽  
Ricci Curvature ◽  
Ricci Flow ◽  
Polynomial Growth ◽  
Holomorphic Functions ◽  
Nonnegative Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Nonnegative Ricci Curvature

Abstract In this paper, we consider holomorphic functions of polynomial growth on complete Kähler manifolds with nonnegative curvature. We explain how their growth orders are related to the asymptotic behavior of Kähler–Ricci flow. The main result is to determine minimal orders of holomorphic functions on gradient Kähler–Ricci expanding solitons with nonnegative Ricci curvature.

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