PROJECTIVE DOMAINS WITH NON-COMPACT AUTOMORPHISM GROUPS I

Title & Authors
PROJECTIVE DOMAINS WITH NON-COMPACT AUTOMORPHISM GROUPS I
Yi, Chang-Woo;

Abstract
Most of domains people have studied are convex bounded projective (or affine) domains. Edith $\small{Soci{\acute{e}}}$-$\small{M{\acute{e}}thou}$ [15] characterized ellipsoid in $\small{{\mathbb{R}}^n}$ by studying projective automorphism of convex body. In this paper, we showed convex and bounded projective domains can be identified from local data of their boundary points using scaling technique developed by several mathematicians. It can be found that how the scaling technique combined with properties of projective transformations is used to do that for a projective domain given local data around singular boundary point. Furthermore, we identify even unbounded or non-convex projective domains from its local data about a boundary point.
Keywords
Language
English
Cited by
1.
Characterizing the unit ball by its projective automorphism group, Geometry & Topology, 2016, 20, 4, 2397
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