article published yes Hana Kourimska author D9B8E14C-3C26-11EA-98F5-1F833DDC885E0000-0001-7841-0091 HeEd department Algebraic Footprints of Geometric Features in Homology project 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. https://research-explorer.ista.ac.at/download/12764/14396/2023_DiscreteGeometry_Kourimska.pdf application/pdfno Springer Nature2023 eng 0179-5376 1432-0444 37292248 00094814800000110.1007/s00454-023-00484-2 70123-153 H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” <i>Discrete and Computational Geometry</i>, vol. 70. Springer Nature, pp. 123–153, 2023. Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” <i>Discrete and Computational Geometry</i>, vol. 70, Springer Nature, 2023, pp. 123–53, doi:<a href="https://doi.org/10.1007/s00454-023-00484-2">10.1007/s00454-023-00484-2</a>. Kourimska, H. (2023). Discrete yamabe problem for polyhedral surfaces. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href="https://doi.org/10.1007/s00454-023-00484-2">https://doi.org/10.1007/s00454-023-00484-2</a> Kourimska H. Discrete yamabe problem for polyhedral surfaces. <i>Discrete and Computational Geometry</i>. 2023;70:123-153. doi:<a href="https://doi.org/10.1007/s00454-023-00484-2">10.1007/s00454-023-00484-2</a> Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. 70, 123–153. Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s00454-023-00484-2">https://doi.org/10.1007/s00454-023-00484-2</a>. H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153. 127642023-03-26T22:01:09Z2025-04-23T08:59:15Z