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

Ivan Izmestiev; Roman Prosanov; Tianqi Wu

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arXiv · 2303.11068

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

Ivan Izmestiev·Roman Prosanov·Tianqi Wu

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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.

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Ivan Izmestiev, Roman Prosanov, Tianqi Wu. 2023-03-20. Prescribed curvature problem for discrete conformality on convex spherical cone-metrics. https://arxiv.org/abs/2303.11068

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