Positivity and completeness of invariant metrics
Taeyong Ahn, Herv\'e Gaussier, Kang-Tae Kim
TL;DR
This paper introduces a method to construct global holomorphic peak functions from local support functions, enabling the demonstration of positivity and completeness of invariant metrics like the Bergman metric on unbounded domains.
Contribution
It provides a novel approach for establishing positivity and completeness of invariant metrics on broad classes of unbounded domains.
Findings
Constructed global holomorphic peak functions from local support functions.
Established positivity of invariant metrics on unbounded domains.
Proved completeness of invariant metrics such as the Bergman metric.
Abstract
We present a method for constructing global holomorphic peak functions from local holomorphic support functions for broad classes of unbounded domains. As an application, we establish a method for showing the positivity and completeness of invariant metrics including the Bergman metric mainly for the unbounded domains.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometry and complex manifolds · Algebraic and Geometric Analysis