Asian Journal of Mathematics

Volume 20 (2016)

Number 5

On a conjecture of Milnor about volumes of simplexes

Pages: 957 – 968

DOI: http://dx.doi.org/10.4310/AJM.2016.v20.n5.a6

Authors

Ren Guo (Department of Mathematics, Oregon State University, Corvallis, Or., U.S.A.)

Feng Luo (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.)

Abstract

We establish the second part of Milnor’s conjecture on the volume of simplexes in hyperbolic and spherical spaces. A characterization of the closure of the space of the angle Gram matrices of simplexes is also obtained.

Keywords

volume, simplex, hyperbolic space, spherical space

2010 Mathematics Subject Classification

52A38, 52A55, 52B11

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