Boundary structure of convex sets in the hyperbolic space

Abstract

We prove some results concerning the boundary of a convex set in $\H^n$. This includes the convergence of curvature measures under Hausdorff convergence of the sets, the study of normal points, and, for convex surfaces, a generalized Gauss equation and some natural characterizations of the regular part of the Gaussian curvature measure.

16 pages

References in corpus (2)

• A stability version of Hölder's inequality
• Metric-measure boundary and geodesic flow on Alexandrov spaces