Fridman's invariant, squeezing functions, and exhausting domains

Abstract

We show that if a bounded domain $\Omega$ is exhausted by a bounded strictly pseudoconvex domain $D$ with $C^2$ boundary, then $\Omega$ is holomorphically equivalent to $D$ or the unit ball, and show that a bounded domain has to be holomorphically equivalent to the unit ball if its Fridman's invariant has certain growth condition near the boundary.

A remark added in the end of the Introduction, and references are updated

References in corpus (6)

• A non-strictly pseudoconvex domain for which the squeezing function tends to one towards the boundary
• Behavior of the squeezing function near h-extendible boundary points
• A characterization of the ball
• Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces
• Characterizing strong pseudoconvexity, obstructions to biholomorphisms, and Lyapunov exponents
• On boundary points at which the squeezing function tends to one