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# 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: http://dx.doi.org/10.4310/MAA.2014.v21.n4.a2

#### Authors

#### 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