Name
Title | ||
|---|---|---|
Discrete Uniformization of Polyhedral Surfaces with Non-positive Curvature and Branched Covers over the Sphere via Hyper-ideal Circle Patterns. |
Abstract | ||
|---|---|---|
With the help of hyper-ideal circle pattern theory, we develop a discrete version of the classical uniformization theorems for closed polyhedral surfaces with non-positive curvature and for surfaces represented as finite branched covers over the Riemann sphere. We show that in these cases discrete uniformization via hyper-ideal circle patterns always exists and is unique. We also propose a numerical algorithm, utilizing convex optimization, that constructs the desired discrete uniformization. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s00454-016-9830-2 | Discrete & Computational Geometry |
Keywords | Field | DocType |
Hyper-ideal circle pattern,Discrete uniformization,Discrete conformal map,Branched cover,Polyhedral surface,Variational principle,52C26,57M50,57M12,52B10 | Uniformization (set theory),Combinatorics,Pattern theory,Curvature,Pure mathematics,Variational principle,Non-positive curvature,Mathematics | Journal |
Volume | Issue | ISSN |
57 | 2 | 0179-5376 |
Citations | PageRank | References |
0 | 0.34 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexander I. Bobenko | 1 | 182 | 17.20 |
| Nikolay Dimitrov | 2 | 0 | 0.34 |
| Stefan Sechelmann | 3 | 0 | 0.34 |