Boundary behavior of the squeezing function near a global extreme point

Abstract

In this paper, we prove that the general ellipsoid $D_P$ is holomorphically homogeneous regular provided that it is a WB-domain. Then, the uniform lower bound for the squeezing function near a $(P,r)$-extreme point is also given.

Keywords:

• Squeezing function
• HHR domain
• automorphism group
• general ellipsoid

AMS Subject Classifications:

• Primary: 32H02
• Secondary: 32M17
• 32F45

Acknowledgments

Part of this work was done while the first author was visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the VIASM for financial support and hospitality. It is a pleasure to thank Hyeseon Kim for stimulating discussions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The third author was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under (grant number 101.99-2019.326). The first author was supported by the research project QG.21.02 “Some problems in operator theory and complex analysis” of Vietnam National University, Hanoi.