On Bergman kernel functions and weak Morse inequalities
Xiaoshan Li, Guokuan Shao, Huan Wang
TL;DR
This paper provides simplified, unified proofs of weak holomorphic Morse inequalities across various complex manifolds using asymptotic Bergman kernel functions and Bochner-Kodaira-Nakano formulas.
Contribution
It introduces a unified approach to proving weak Morse inequalities on diverse complex manifolds based on Bergman kernel asymptotics.
Findings
Unified proofs for weak Morse inequalities across multiple manifold types.
Application of asymptotic Bergman kernel functions in complex geometry.
Demonstration of the effectiveness of Bochner-Kodaira-Nakano formulas in this context.
Abstract
We give simple and unified proofs of weak holomorhpic Morse inequalities on complete manifolds, -convex manifolds, pseudoconvex domains, weakly -complete manifolds and covering manifolds. This paper is essentially based on the asymptotic Bergman kernel functions and the Bochner-Kodaira-Nakano formulas.
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Taxonomy
TopicsAnalytic and geometric function theory · Geometry and complex manifolds · Holomorphic and Operator Theory