The infimum of the volumes of convex polytopes of any given facet areas is 0-Reference-Cited by-同舟云学术

The infimum of the volumes of convex polytopes of any given facet areas is 0

Published:2014-12-01 Issue:4 Volume:51 Page:466-519
ISSN:0081-6906
Container-title:Studia Scientiarum Mathematicarum Hungarica
language:
Short-container-title:

Author:

Abrosimov N.,Makai E.¹,Mednykh A.,Nikonorov Yu.²,Rote G.³

Affiliation:

1. 3 Hungarian Academy of Sciences A. Rényi Institute of Mathematics H-1364 Budapest Pf. 127 Hungary

2. 4 South Mathematical Institute of the V. S. C. of the Russian Academy of Sciences Vladikavkaz Markus Str. 22 362027 Russia

3. 5 Freie Universität Berlin Institut für Informatik Takustr. 9 14159 Berlin Germany

Abstract

We prove the theorem mentioned in the title for ℝnwheren≧ 3. The case of the simplex was known previously. Also the casen= 2 was settled, but there the infimum was some well-defined function of the side lengths. We also consider the cases of spherical and hyperbolicn-spaces. There we give some necessary conditions for the existence of a convex polytope with given facet areas and some partial results about sufficient conditions for the existence of (convex) tetrahedra.

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

Link

https://www.akademiai.com/doi/pdf/10.1556/sscmath.51.2014.4.1292

Reference62 articles.

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