Limit polygons of convex domains in the projective plane

Abstract

For any sequence of properly convex domains in the real projective plane such that the zeros of Pick differentials have bounded multiplicity and get further and further apart, we determined all Hausdorff limit domains that one can obtain after normalizing each member of the sequence by a projective transformation. We then show that the result can be applied to convex domains generated by projective triangular reflection groups.

arXiv comment19 pages, 5 figures. Comments welcome

References in corpus (2)

• Locally homogeneous geometric manifolds
• On the Hilbert geometry of simplicial Tits sets