Rigidity of complex convex divisible sets

2013/08/19 by Zimmer, Andrew M. · 1 citation
#22E40 #32C15 #53A20 #53C24 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1308.4116

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 C¹ 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 C¹ boundary are the projective balls.

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