Methods and Applications of Analysis

Volume 21 (2014)

Number 4

Special issue dedicated to the 60th birthday of Stephen S.-T. Yau: Part II

Guest editors: John Erik Fornæss, Xiaojun Huang, Song-Ying Li, Yat Sun Poon, Wing Shing Wong, and Zhouping Xin

On boundary accumulation points of a convex domain in $\mathbb{C}^n$

Pages: 427 – 440

DOI: https://dx.doi.org/10.4310/MAA.2014.v21.n4.a2

Authors

Lina Lee (Department of Mathematics, University of California at Riverside)

Bradley Thomas (Department of Natural and Mathematical Sciences, California Baptist University, Riverside, Calif., U.S.A.)

Bun Wong (Department of Mathematics, University of California at Riverside)

Abstract

In this paper we show that, for a smoothly bounded convex domain $\Omega \subset \mathbb{C}^n$, if there is $\{ \phi_j \} \subset \mathrm{Aut}(\Omega)$ such that $\phi_j (z)$ converges to some boundary point non-tangentially for all $z \in \Omega$, then there does not exist a non-trivial analytic disc on $\partial \Omega$ through any boundary orbit accumulation points.

Keywords

automorphism group, convex domains, invariant metrics/measures

2010 Mathematics Subject Classification

32F18, 32F45

Full Text (PDF format)

Published 9 October 2014