A Psh Hopf Lemma for Domains with Cusp Conditions
Bo-Yong Chen, Yuanpu Xiong
TL;DR
This paper establishes a psh Hopf lemma for domains with cusp conditions using Green function estimates, leading to a negative psh exhaustion function with growth estimates on pseudoconvex domains.
Contribution
It introduces a new psh Hopf lemma for cusp domains and constructs a global growth estimate for exhaustion functions on pseudoconvex domains.
Findings
Established a psh Hopf lemma for cusp domains
Derived a sharp Green function estimate for planar cusps
Constructed a negative psh exhaustion function with growth bounds
Abstract
We obtain a psh Hopf lemma for domains satisfying certain cusp conditions by using a sharp estimate for the Green function of a planar cusp along the axis. As an application, we obtain a negative psh exhaustion function with certain global growth estimate on a pseudoconvex domain with H\"{o}lder boundary.
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Taxonomy
TopicsAnalytic and geometric function theory · Advanced Mathematical Modeling in Engineering · Holomorphic and Operator Theory