Asian Journal of Mathematics

Volume 20 (2016)

Number 5

On a conjecture of Milnor about volumes of simplexes

Pages: 957 – 968



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.)


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.


volume, simplex, hyperbolic space, spherical space

2010 Mathematics Subject Classification

52A38, 52A55, 52B11

Published 22 February 2017