Fundamental domains of convex projective structures
by
Jaejeong Lee
UC Davis

Convex (or properly convex) projective structures on manifolds share many common features with non-positively curved metrics. The lack of invariant metrics, however, makes it harder to study them. For example, some of the well-known facts about fundamental domains in the case of constant curvature geometries are no longer obvious in projective geometry. In my talk, I will show that every properly convex projective structure admits a convex fundamental polyhedron, which is the Dirichlet domain with respect to a certain distance-like function. The proof makes an essential use of the solution (by Cheng and Yau) of Calabi's conjecture on complete hyperbolic affine spheres and the duality relation between them.

Date received: February 14, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawj-16.