Simplicial Ricci Flow

Topological Signatures of Singularities in Simplicial Ricci Flow

We apply the methods of persistent homology to a selection of two and three– dimensional geometries evolved by simplicial Ricci flow. To implement persistent homology, we construct a triangular mesh for a sample of points. The scalar curvature along the edges of the triangulation, computed as an average of scalar curvatures at the endpoints of the edges, serves as a filtration parameter at each...

Applications of Persistent Homology to Simplicial Ricci Flow

Paul M. Alsing∗1, Howard A. Blair†2, Matthew Corne‡1, Gordon Jones§3, Warner A. Miller¶4, Konstantin Mischaikow‖5 and Vidit Nanda∗∗6 Air Force Research Laboratory, Information Directorate, Rome, NY 13441 Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY 13244 Department of Computer Science, University of Michigan, Ann Arbor, MI 48109 Department of Phys...

Ricci Lower Bound for Kähler–ricci Flow

Ricci Flow Gravity

A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gravity. In particular there is no adjustable coupling constant. For the solar ...

Generalized Discrete Ricci Flow

Surface Ricci flow is a powerful tool to design Riemannian metrics by user defined curvatures. Discrete surface Ricci flow has been broadly applied for surface parameterization, shape analysis, and computational topology. Conventional discrete Ricci flow has limitations. For meshes with low quality triangulations, if high conformality is required, the flow may get stuck at the local optimum of ...