Outputs (5)

Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature (2020)
Journal Article
Cushing, D., Kamtue, S., Liu, S., Muench, F., & Peyerimhoff, N. (2020). Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature. Advances in Mathematics, 360, Article 107188. https://doi.org/10.1016/j.aim.2020.107188

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 sharp graphs (hypercubes, cocktail party graphs, even-dimensional demi-cub... Read More about Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature.

Quartic graphs which are Bakry-Émery curvature sharp (2019)
Journal Article
Cushing, D., Kamtue, S., Peyerimhoff, N., & Watson May, L. (2020). Quartic graphs which are Bakry-Émery curvature sharp. Discrete Mathematics, 343(3), Article 111767. https://doi.org/10.1016/j.disc.2019.111767

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 computer classification by F. Gurr and L. Watson May and a combinatorial cas... Read More about Quartic graphs which are Bakry-Émery curvature sharp.

Long-Scale Ollivier Ricci Curvature of Graphs (2019)
Journal Article
Cushing, D., & Kamtue, S. (2019). Long-Scale Ollivier Ricci Curvature of Graphs. Analysis and Geometry in Metric Spaces, 7(1), 22-44. https://doi.org/10.1515/agms-2019-0003

We study the long-scale Ollivier Ricci curvature of graphs as a function of the chosen idleness. Similarly to the previous work on the short-scale case, we show that this idleness function is concave and piecewise linear with at most 3 linear parts.... Read More about Long-Scale Ollivier Ricci Curvature of Graphs.

Bakry-Émery Curvature Functions on Graphs (2018)
Journal Article
Cushing, D., Liu, S., & Peyerimhoff, N. (2020). Bakry-Émery Curvature Functions on Graphs. Canadian Journal of Mathematics, 72(1), 89-143. https://doi.org/10.4153/cjm-2018-015-4

We study local properties of the Bakry-Émery curvature function KG,x:(0,∞]→R at a vertex x of a graph G systematically. Here KG,x(N) is defined as the optimal curvature lower bound K in the Bakry-Émery curvature-dimension inequality CD(K,N) that x sa... Read More about Bakry-Émery Curvature Functions on Graphs.

Free functions with symmetry (2017)
Journal Article
Cushing, D., Pascoe, J., & Tully-Doyle, R. (2018). Free functions with symmetry. Mathematische Zeitschrift, 289(3-4), 837-857. https://doi.org/10.1007/s00209-017-1977-x

In 1936, Margarete C. Wolf showed that the ring of symmetric free polynomials in two or more variables is isomorphic to the ring of free polynomials in infinitely many variables. We show that Wolf’s theorem is a special case of a general theory of th... Read More about Free functions with symmetry.