Alexandrov spaces with maximal radius

Abstract

In this paper we prove several rigidity theorems related to and including Lytchak's problem.The focus is on Alexandrov spaces with curv ≥ 1, nonempty boundary, and maximal radius π 2 .We exhibit many such spaces that indicate that this class is remarkably flexible.Nevertheless, we also show that when the boundary is either geometrically or topologically spherical, then it is possible to obtain strong rigidity results.In contrast to this one can show that with general lower curvature bounds and strictly convex boundary only cones can have maximal radius.We also mention some connections between our problems and the positive mass conjectures.

Locations

• eScholarship (California Digital Library) - View - PDF
• arXiv (Cornell University) - View - PDF
• Geometry & Topology - View