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arXiv · 1308.4116

Rigidity of complex convex divisible sets

Andrew M. Zimmer
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Abstract

An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts co-compactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are strictly convex, have $C^1$ boundary, and have word hyperbolic dividing group. In this paper we study a notion of convexity in complex projective space and show that the only divisible complex convex sets with $C^1$ boundary are the projective balls.

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Andrew M. Zimmer. 2013-08-19. Rigidity of complex convex divisible sets. https://arxiv.org/abs/1308.4116

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