Abstract
A notion of discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a unique hyperbolic polyhedral metric with a given discrete curvature satisfying Gauss–Bonnet formula. Furthermore, the hyperbolic polyhedral metric with given curvature can be obtained using a discrete Yamabe flow with surgery. In particular, each hyperbolic polyhedral metric on a closed surface with negative Euler characteristic is discrete conformal to a unique hyperbolic metric.
Original language | English (US) |
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Pages (from-to) | 431-466 |
Number of pages | 36 |
Journal | Journal of Differential Geometry |
Volume | 109 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2018 |
All Science Journal Classification (ASJC) codes
- Analysis
- Algebra and Number Theory
- Geometry and Topology
Keywords
- And Delaunay triangulation.
- Discrete Yamabe flow
- Discrete conformality
- Discrete uniformization
- Hyperbolic metrics
- Variational principle