Outputs (5)

Minimizing length of billiard trajectories in hyperbolic polygons (2018)
Journal Article
Parker, J. R., Peyerimhoff, N., & Siburg, K. F. (2018). Minimizing length of billiard trajectories in hyperbolic polygons. Conformal Geometry and Dynamics, 22, 315-332. https://doi.org/10.1090/ecgd/328

Closed billiard trajectories in a polygon in the hyperbolic plane can be coded by the order in which they hit the sides of the polygon. In this paper, we consider the average length of cyclically related closed billiard trajectories in ideal hyperbol... Read More about Minimizing length of billiard trajectories in hyperbolic polygons.

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.

Ollivier-Ricci idleness functions of graphs (2018)
Journal Article
Bourne, D., Cushing, D., Liu, S., Muench, F., & Peyerimhoff, N. (2018). Ollivier-Ricci idleness functions of graphs. SIAM Journal on Discrete Mathematics, 32(2), 1408-1424. https://doi.org/10.1137/17m1134469

We study the Ollivier--Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most three linear parts, and at most two linear parts in the case of a regular graph. W... Read More about Ollivier-Ricci idleness functions of graphs.

Eigenvalue ratios of non-negatively curved graphs (2018)
Journal Article
Liu, S., & Peyerimhoff, N. (2018). Eigenvalue ratios of non-negatively curved graphs. Combinatorics, Probability and Computing, 27(5), 829-850. https://doi.org/10.1017/s0963548318000214

We derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality CD(0, ∞). This estimate is independent of the size of the graph and provides a general method to obtain higher-order spectral esti... Read More about Eigenvalue ratios of non-negatively curved graphs.

Bakry–Émery curvature and diameter bounds on graphs (2018)
Journal Article
Liu, S., Münch, F., & Peyerimhoff, N. (2018). Bakry–Émery curvature and diameter bounds on graphs. Calculus of Variations and Partial Differential Equations, 57(2), Article 67. https://doi.org/10.1007/s00526-018-1334-x

We prove finiteness and diameter bounds for graphs having a positive Ricci-curvature bound in the Bakry–Émery sense. Our first result using only curvature and maximal vertex degree is sharp in the case of hypercubes. The second result depends on an a... Read More about Bakry–Émery curvature and diameter bounds on graphs.