We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Combinatorial Curvature Flows for Generalized Circle Packings on Surfaces with Boundary.
- Authors
Xu, Xu; Zheng, Chao
- Abstract
In this paper, we investigate the deformation of generalized circle packings on ideally triangulated surfaces with boundary, which is the |$(-1,-1,-1)$| -type generalized circle packing metric introduced by Guo and Luo [ 16 ]. To find hyperbolic metrics on surfaces with totally geodesic boundaries of prescribed lengths, we introduce combinatorial Ricci flow and combinatorial Calabi flow for generalized circle packings on ideally triangulated surfaces with boundary. Then we prove the longtime existence and global convergence for the solutions of these combinatorial curvature flows, which provide effective algorithms for finding hyperbolic metrics on surfaces with totally geodesic boundaries of prescribed lengths.
- Subjects
CURVATURE; RICCI flow; CIRCLE; GEODESICS
- Publication
IMRN: International Mathematics Research Notices, 2023, Vol 2023, Issue 20, p17704
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad026