THE INFIMUM OF THE VOLUMES OF CONVEX POLYTOPES OF ANY GIVEN FACET AREAS IS 0

被引：1

作者：

Abrosimov, N. V. ^{[1
,2
]}

Makai, E., Jr. ^{[3
]}

Mednykh, A. D. ^{[1
,2
]}

Nikonorov, Yu. G. ^{[4
]}

Rote, G. ^{[5
]}

机构：

[1] Sobolev Inst Math, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

[3] Hungarian Acad Sci, A Renyi Inst Math, H-1364 Budapest, Hungary

[4] Russian Acad Sci, VSC, South Math Inst, Vladikavkaz 362027, Russia

[5] Free Univ Berlin, Inst Informat, D-14159 Berlin, Germany

来源：

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA | 2014年 / 51卷 / 04期

关键词：

convex polytopes; volume; Euclidean; spherical; hyperbolic spaces; MAXIMAL VOLUME;

D O I：

10.1556/SScMath.51.2014.4.1292

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the theorem mentioned in the title for R-n where n >= 3. The case of the simplex was known previously. Also the case n = 2 was settled, but there the infimum was some well-defined function of the side lengths. We also consider the cases of spherical and hyperbolic n-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.

引用

页码：466 / 519

页数：54

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