9 citations · 15 across the 6 of their papers we have counts for
6 papers
Optimal embedding and spectral gap of a finite graph
Takumi Gomyou, Toshimasa Kobayashi, Takefumi Kondo +1
We introduce a new optimization problem regarding embeddings of a graph into a Euclidean space and discuss its relation to the two, mutually dual, optimizations problems introduced…
Fixed-point property for affine actions on a Hilbert space
Shin Nayatani
Gromov showed that for fixed, arbitrarily large C, any uniformly C-Lipschitz affine action of a random group in his graph model on a Hilbert space has a fixed point. We announce a…
Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian
Shin Nayatani, Toshihiro Shoda
In this paper, we settle in the affirmative the Jakobson-Levitin-Nadirashvili-Nigam-Polterovich conjecture, stating that a certain singular metric on the Bolza surface, with area n…
Quaternionic CR Geometry
Hiroyuki Kamada, Shin Nayatani
Modelled on a real hypersurface in a quaternionic manifold, we introduce a quaternionic analogue of CR structure, called quaternionic CR structure. We define the strong pseudoconve…
N-step energy of maps and fixed-point property of random groups
Hiroyasu Izeki, Takefumi Kondo, Shin Nayatani
We prove that a random group of the graph model associated with a sequence of expanders has fixed-point property for a certain class of CAT(0) spaces. We use Gromov's criterion for…
Combinatorial harmonic maps and discrete-group actions on Hadamard spaces
Hiroyasu Izeki, Shin Nayatani
We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properl…