{"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"page":"123-153","oa_version":"Published Version","license":"https://creativecommons.org/licenses/by/4.0/","isi":1,"publisher":"Springer Nature","abstract":[{"lang":"eng","text":"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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"isi":["000948148000001"]},"oa":1,"has_accepted_license":"1","day":"01","date_updated":"2023-10-04T11:46:48Z","year":"2023","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"article_type":"original","intvolume":"        70","publication":"Discrete and Computational Geometry","doi":"10.1007/s00454-023-00484-2","title":"Discrete yamabe problem for polyhedral surfaces","project":[{"_id":"26AD5D90-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I04245","name":"Algebraic Footprints of Geometric Features in Homology"}],"date_published":"2023-07-01T00:00:00Z","file_date_updated":"2023-10-04T11:46:24Z","acknowledgement":"Open access funding provided by the Austrian Science Fund (FWF). This research was supported by the FWF grant, Project number I4245-N35, and by the Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID 195170736 - TRR109.","date_created":"2023-03-26T22:01:09Z","scopus_import":"1","month":"07","author":[{"orcid":"0000-0001-7841-0091","last_name":"Kourimska","first_name":"Hana","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","full_name":"Kourimska, Hana"}],"citation":{"ama":"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>","chicago":"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>.","apa":"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>","mla":"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>.","ista":"Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. 70, 123–153.","ieee":"H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” <i>Discrete and Computational Geometry</i>, vol. 70. Springer Nature, pp. 123–153, 2023.","short":"H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153."},"status":"public","_id":"12764","file":[{"content_type":"application/pdf","success":1,"creator":"dernst","file_name":"2023_DiscreteGeometry_Kourimska.pdf","access_level":"open_access","checksum":"cdbf90ba4a7ddcb190d37b9e9d4cb9d3","file_size":1026683,"relation":"main_file","date_created":"2023-10-04T11:46:24Z","file_id":"14396","date_updated":"2023-10-04T11:46:24Z"}],"publication_status":"published","quality_controlled":"1","volume":70,"department":[{"_id":"HeEd"}],"type":"journal_article","article_processing_charge":"Yes (via OA deal)","ddc":["510"]}