Sufficiency of simplex inequalities

DOI10.1090/proc12756zbMath1336.51014arXiv1309.4534OpenAlexW2015598435MaRDI QIDQ2790206

Shuzo Izumi

Publication date: 3 March 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.4534

zbMATH Keywords

volumesimplextriangle inequalityfacetcontentconverse of the triangle inequality

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area and volume in real or complex geometry (51M25) Elementary problems in Euclidean geometries (51M04) Geometric constructions in real or complex geometry (51M15) Inequalities and extremum problems in real or complex geometry (51M16)

Related Items (5)

Anothern-Dimensional Generalization of Pompeiu’s Theorem ⋮ Pompeiu-like theorems for the medians of a simplex ⋮ Recovering a circumscriptible tetrahedron from its face areas ⋮ The median triangle theorem as an entrance to certain issues in higher-dimensional geometry ⋮ The existence of triangles, tetrahedra, and higher-dimensional simplices with prescribed exradii

Cites Work

• The Minkowski problem for polytopes
• Convex Bodies The Brunn-MinkowskiTheory

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