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Discrete Yamabe problem for polyhedral surfaces

Authors :
Kouřimská, Hana Dal Poz
Publication Year :
2021

Abstract

We study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical singularity of a polyhedral surface as the quotient of the angle defect and the area of the Voronoi cell corresponding to the singularity. We divide polyhedral surfaces into discrete conformal classes using a generalization of discrete conformal equivalence pioneered by Feng Luo. We subsequently show that, in every discrete conformal class, there exists a polyhedral surface with constant discrete Gaussian curvature. We also provide explicit examples to demonstrate that this surface is in general not unique.<br />Comment: 31 pages, 11 figures, submitted to the Journal of Discrete and Computational Geometry

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2103.15693
Document Type :
Working Paper
Full Text :
https://doi.org/10.1007/s00454-023-00484-2