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On the comparison of the Fridman invariant and the squeezing function
Complex Variables and Elliptic Equations ( IF 0.9 ) Pub Date : 2020-12-15 , DOI: 10.1080/17476933.2020.1851210
Feng Rong 1 , Shichao Yang 1
Affiliation  

Let D be a bounded domain in Cn, n1. In this paper, we study two biholomorphic invariants on D, the Fridman invariant eD(z) and the squeezing function sD(z). More specifically, we study two questions about the quotient invariant mD(z)=sD(z)/eD(z): (1) If mD(z0)=1 for some z0D, is D biholomorphic to the unit ball? (2) Is mD(z) constantly equal to 1? We answer both questions negatively.



中文翻译:

弗里德曼不变量与挤压函数的比较

D为有界域Cn,n1. 在本文中,我们研究了D上的两个双全纯不变量,即 Fridman 不变量eD(z)和挤压功能sD(z). 更具体地说,我们研究了关于商不变量的两个问题 D(z)=sD(z)/eD(z): (1) 如果D(z0)=1对于一些z0D, D对单位球是双全纯的吗?(2) 是D(z)始终等于 1?我们否定地回答这两个问题。

更新日期:2020-12-15
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