PreprintCC BY 4.0arXiv
Prescribed combinatorial curvature beyond positivity for spherical vertex scalings on the sphere
Abstract
Let (S,V) be a marked 2-sphere with |V|≥3, 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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BibTeX
@misc{liu2026prescribed,
title = {{Prescribed combinatorial curvature beyond positivity for spherical vertex scalings on the sphere}},
author = {Chen Liu and Xu Xu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04478},
eprint = {2611.04478},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04478},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Prescribed combinatorial curvature beyond positivity for spherical vertex scalings on the sphere
AU - Chen Liu
AU - Xu Xu
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04478
UR - https://arxiv.org/abs/2611.04478
AB - Let (S,V) be a marked 2-sphere with |V|≥3, 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.
ER -