7 papers
Transportation Distance between Probability Measures on the Infinite Regular Tree
Pakawut Jiradilok, Supanat Kamtue
In the infinite regular tree with , we consider families , indexed by vertices and nonnegative integers ("discrete time…
Bonnet-Myers sharp graphs of diameter three
Supanat Kamtue
Regular graphs which are Bonnet-Myers sharp (in the sense of Ollivier Ricci curvature) and self-centered have been completely classified, and it is a natural question whether the c…
A note on a Bonnet-Myers type diameter bound for graphs with positive entropic Ricci curvature
Supanat Kamtue
An equivalent definition of entropic Ricci curvature on discrete spaces was given in terms of the global gradient estimate. With a particular choice of the density function , we…
Quartic graphs which are Bakry-Émery curvature sharp
David Cushing, Supanat Kamtue, Norbert Peyerimhoff +1
We give a classification of all connected quartic graphs which are (infinity) curvature sharp in all vertices with respect to Bakry-Émery curvature. The result is based on a comput…
Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature
David Cushing, Supanat Kamtue, Jack Koolen +3
We introduce the notion of Bonnet-Myers and Lichnerowicz sharpness in the Ollivier Ricci curvature sense. Our main result is a classification of all self-centered Bonnet-Myers shar…
Combinatorial, Bakry-Émery, Ollivier's Ricci curvature notions and their motivation from Riemannian geometry
Supanat Kamtue
In this survey, we study three different notions of curvature that are defined on graphs, namely, combinatorial curvature, Bakry-Émery curvature, and Ollivier's Ricci curvature. Fo…