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

Ivan Izmestiev; Roman Prosanov; Tianqi Wu

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

Metric Geometry 2023-11-30 v2 Geometric Topology

Authors: Ivan Izmestiev , Roman Prosanov , Tianqi Wu

Abstract

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 $\kappa: V \rightarrow (0, 2\pi)$ 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 Luo and Tian.

Keywords

conformal geometry sphere packings and spherical designs differential geometry

Cite

@article{arxiv.2303.11068,
  title  = {Prescribed curvature problem for discrete conformality on convex spherical cone-metrics},
  author = {Ivan Izmestiev and Roman Prosanov and Tianqi Wu},
  journal= {arXiv preprint arXiv:2303.11068},
  year   = {2023}
}

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