Open Access
Spring 1999 Total curvatures of convex hypersurfaces in hyperbolic space
Alexandr A. Borisenko, Vicente Miquel
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Illinois J. Math. 43(1): 61-78 (Spring 1999). DOI: 10.1215/ijm/1255985337


We give sharp upper estimates for the difference circumradius minus inradius and for the angle between the radial vector (respect to the center of an inball) and the normal to the boundary of a compact $h$-convex domain in the hyperpolic space. We apply these estimates to get the limit at the infinity for the quotients Volume/Area and (Total $k$-mean curvature)/Area of a family of $h$-convex domains which expand over the whole space. The theorem for the first quotient gives an extension to arbitrary dimension of a result of Santaló and Yañez for the hyperbolic plane.


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Alexandr A. Borisenko. Vicente Miquel. "Total curvatures of convex hypersurfaces in hyperbolic space." Illinois J. Math. 43 (1) 61 - 78, Spring 1999.


Published: Spring 1999
First available in Project Euclid: 19 October 2009

zbMATH: 0981.53046
MathSciNet: MR1665641
Digital Object Identifier: 10.1215/ijm/1255985337

Primary: 53C65
Secondary: 53C40

Rights: Copyright © 1999 University of Illinois at Urbana-Champaign

Vol.43 • No. 1 • Spring 1999
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