A characterization of the ball
Klas Diederich, John Erik Forn{\ae}ss, Erlend Forn{\ae}ss Wold
TL;DR
This paper investigates specific bounded domains with smooth boundaries and analyzes their squeezing functions to establish conditions under which these domains are biholomorphic to the unit ball.
Contribution
It provides a characterization of domains biholomorphic to the ball based on properties of their squeezing functions and boundary smoothness.
Findings
Domains with certain smoothness conditions are biholomorphic to the ball.
Squeezing functions serve as key tools in characterizing the domain's geometry.
The paper establishes new criteria linking boundary smoothness and biholomorphic equivalence.
Abstract
We study bounded domains with certain smoothness conditions and the properties of their squeezing functions in order to prove that the domains are biholomorphic to the ball.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Geometry and complex manifolds