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arXiv · 2611.04478

Prescribed combinatorial curvature beyond positivity for spherical vertex scalings on the sphere

Chen Liu·Xu Xu
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Abstract

Let $(S,V)$ be a marked 2-sphere with $|V|\ge3$, and fix a spherical discrete conformal class. Izmestiev-Prosanov-Wu proved existence and uniqueness for positive prescribed combinatorial curvature in the spherical discrete conformal class on $(S,V)$. In this paper, we identify a region of prescribed combinatorial curvature vectors, allowing some negative components, for which existence still holds.

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Chen Liu, Xu Xu. 2026-11-03. Prescribed combinatorial curvature beyond positivity for spherical vertex scalings on the sphere. https://arxiv.org/abs/2611.04478

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