Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2017; 32(1): 165-173

Online first article January 18, 2017      Printed January 31, 2017

https://doi.org/10.4134/CKMS.c160052

Copyright © The Korean Mathematical Society.

Asymptotic foliations of quasi-homogeneous convex affine domains

Kyeonghee Jo

Mokpo National Maritime University

Abstract

In this paper, we prove that the automorphism group of a quasi-homogeneous properly convex affine domain in $\mathbb R^n$ acts transitively on the set of all the extreme points of the domain. This set is equal to the set of all the asymptotic cone points coming from the asymptotic foliation of the domain and thus it is a homogeneous submanifold of $\mathbb R^n$.

Keywords: asymptotic cone, foliation, quasi-homogeneous domain

MSC numbers: 52A20, 53C12, 57N16, 57S25

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