Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 46, No. 2, pp. 609614 (2005) 

On the monotonicity of the volume of hyperbolic convex polyhedraKároly BezdekDepartment of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Ab Canada T2N 1N4; email: bezdek@math.ucalgary.caAbstract: We give a proof of the monotonicity of the volume of nonobtuseangled compact convex polyhedra in terms of their dihedral angles. More exactly we prove the following. Let $P$ and $Q$ be nonobtuseangled compact convex polydedra of the same simple combinatorial type in hyperbolic $3$space. If each (inner) dihedral angle of $Q$ is at least as large as the corresponding (inner) dihedral angle of $P$, then the volume of $P$ is at least as large as the volume of $Q$. Moreover, we extend this result to nonobtuseangled hyperbolic simplices of any dimension. Keywords: hyperbolic nonobtuseangled convex polyhedra, KoebeAndreev Thurston theorem, hyperbolic volume Classification (MSC2000): 52A55, 52C29 Full text of the article:
Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.
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