A comparison of two biholomorphic invariants

TL;DR

This paper compares the Fridman invariant and the squeezing function, two biholomorphic invariants, demonstrating their equal effectiveness in determining boundary geometry of bounded domains when boundary behavior is known.

Contribution

It establishes the equivalence of the Fridman invariant and the squeezing function in boundary geometry determination under certain conditions.

Findings

Both invariants can determine boundary geometry if boundary behavior is known.

The Fridman invariant is the dual of the squeezing function.

They are equally capable of characterizing boundary geometry.

Abstract

The Fridman invariant, which is a biholomorphic invariant on Kobayashi hyperbolic manifolds, can be seen as the dual of the much studied squeezing function. We compare this pair of invariants by showing that they are both equally capable of determining the boundary geometry of a bounded domain if their boundary behaviour is apriori known.