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.
Veronelli, G. (2019). Boundary structure of convex sets in the hyperbolic space. MONATSHEFTE FÜR MATHEMATIK, 188(3), 567-586 [10.1007/s00605-018-1194-7].
Boundary structure of convex sets in the hyperbolic space
Veronelli, G
2019
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.
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