Prescribed curvature problem for discrete conformality on convex spherical cone-metrics

2023/03/20 by Izmestiev, Ivan, Prosanov, Roman, Wu, Tianqi · 1 citation
#30F45 #52B10 #52B70 #52C26 #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2303.11068

Abstract

Let S be the 2-sphere and V ⊂ S be a finite set of at least three points. We show that for each function κ: V → (0, 2π) satisfying elementary necessary conditions, in each discrete conformal class of spherical cone-metrics there exists a unique metric realizing κ as its discrete curvature. This can be seen as a discrete version of a result of Luo and Tian.

Cited by

• Spherical orthogonal ring patterns on surfaces and modified combinatorial total geodesic curvatures

Related

• Metrics of constant curvature 1 with three conical singularities on 2-sphere
• Discrete Conformal Deformation: Algorithm and Experiments
• Geometric structure and existence of reducible spherical conical metrics
• Parabolic bundles and spherical metrics
• Conformal metrics of the ball with constant σ_k-curvature and constant boundary mean curvature