Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2005; 42(3): 485-498

Printed May 1, 2005

Copyright © The Korean Mathematical Society.

Differentiability of quasi-homogeneous domains

Kyeonghee Jo

Seoul National University

Abstract

In this article we show that every quasi-homogeneous convex affine domain whose boundary is everywhere differentiable except possibly at a finite number of points is either homogeneous or covers a compact affine manifold. Actually we show that such a domain must be a non-elliptic strictly convex cone if it is not homogeneous.

Keywords: quasi-homogeneous, homogeneous, divisible, strictly convex, affinely flat manifold

MSC numbers: 52A20, 53C24, 57N16