On the comparison of the Fridman invariant and the squeezing function

2020/11/25 by Rong, Feng, Yang, Shichao
#32F45 #32H02 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.12464

Abstract

Let D be a bounded domain in ℂⁿ, n≥ 1. In this paper, we study two biholomorphic invariants on D, the Fridman invariant e_D(z) and the squeezing function s_D(z). More specifically, we study the following two questions about the quotient invariant m_D(z)=s_D(z)/e_D(z): 1) If m_D(z₀)=1 for some z₀∈ D, is D biholomorphic to the unit ball? 2) Is m_D(z) constantly equal to 1? We answer both questions negatively.

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