34 citations · 172 across the 30 of their papers we have counts for
13 papers · 1 filter
Timelike Hilbert geometry of the spherical simplex
Athanase Papadopoulos, Sumio Yamada
We prove the following result on the timelike spherical Hilbert geometry of simplices: Let be a simplex on the 2-sphere and the antipodal simplex. We show that th…
Gravitational Solitons and Complete Ricci Flat Riemannian Manifolds of Infinite Topological Type
Marcus Khuri, Martin Reiris, Gilbert Weinstein +1
We present several new space-periodic solutions of the static vacuum Einstein equations in higher dimensions, both with and without black holes, having Kasner asymptotics. These la…
Timelike Hilbert and Funk geometries
Athanase Papadopoulos, Sumio Yamada
A timelike space is a Hausdorff topological space equipped with a partial order relation and a distance function satisfying a collection of axioms including a set of compat…
Local and Global Aspects of Weil-Petersson Geometry
Sumio Yamada
This is a survey paper on the topic of Weil-Petersson geometry of Teichmuller spaces. Even though historically the subject has been developed as a branch of complex analysis, the t…
Convex bodies in Euclidean and Weil-Petersson geometries
Sumio Yamada
On a convex body in a Euclidean space, we introduce a new variational formulation for its Funk metric, a Finsler metric compatible with the tautological Finsler structure of the co…
Total Curvature of Graphs after Milnor and Euler
Robert Gulliver, Sumio Yamada
We define a new notion of total curvature, called net total curvature, for finite graphs embedded in Rn, and investigate its properties. Two guiding principles are given by Milnor'…