Ricci Curvature on Polyhedral Surfaces via Optimal Transportation
AbstractThe problem of correctly defining geometric objects, such as the curvature, is a hard one in discrete geometry. In 2009, Ollivier defined a notion of curvature applicable to a wide category of measured metric spaces, in particular to graphs. He named it coarse Ricci curvature because it coincides, up to some given factor, with the classical Ricci curvature, when the space is a smooth manifold. Lin, Lu and Yau and Jost and Liu have used and extended this notion for graphs, giving estimates for the curvature and, hence, the diameter, in terms of the combinatorics. In this paper, we describe a method for computing the coarse Ricci curvature and give sharper results, in the specific, but crucial case of polyhedral surfaces.
Scifeed alert for new publicationsNever miss any articles matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now
Loisel, B.; Romon, P. Ricci Curvature on Polyhedral Surfaces via Optimal Transportation. Axioms 2014, 3, 119-139.
Loisel B, Romon P. Ricci Curvature on Polyhedral Surfaces via Optimal Transportation. Axioms. 2014; 3(1):119-139.Chicago/Turabian Style
Loisel, Benoît; Romon, Pascal. 2014. "Ricci Curvature on Polyhedral Surfaces via Optimal Transportation." Axioms 3, no. 1: 119-139.