Prescribed curvature problem for discrete conformality on convex spherical cone-metrics. (English) Zbl 1531.30032
Summary: Let \(S\) be the 2-sphere and \(V \subset S\) be a finite set of at least three points. We show that for each function \(\kappa : V \to(0, 2 \pi)\) satisfying elementary necessary conditions, in each discrete conformal class of spherical cone-metrics there exists a unique metric realizing \(\kappa\) as its discrete curvature. This can be seen as a discrete version of a result of F. Luo and G. Tian [Proc. Am. Math. Soc. 116, No. 4, 1119–1129 (1992; Zbl 0806.53012)].
MSC:
| 30F45 | Conformal metrics (hyperbolic, Poincaré, distance functions) |
| 52B10 | Three-dimensional polytopes |
| 52B70 | Polyhedral manifolds |
| 52C26 | Circle packings and discrete conformal geometry |
Citations:
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