---
_id: '12764'
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.
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.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Hana
  full_name: Kourimska, Hana
  id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
  last_name: Kourimska
  orcid: 0000-0001-7841-0091
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>
  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>
  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>.
  ieee: H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” <i>Discrete
    and Computational Geometry</i>, vol. 70. Springer Nature, pp. 123–153, 2023.
  ista: Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete
    and Computational Geometry. 70, 123–153.
  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>.
  short: H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153.
corr_author: '1'
date_created: 2023-03-26T22:01:09Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2025-04-23T08:59:15Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-023-00484-2
external_id:
  isi:
  - '000948148000001'
  pmid:
  - '37292248'
file:
- access_level: open_access
  checksum: cdbf90ba4a7ddcb190d37b9e9d4cb9d3
  content_type: application/pdf
  creator: dernst
  date_created: 2023-10-04T11:46:24Z
  date_updated: 2023-10-04T11:46:24Z
  file_id: '14396'
  file_name: 2023_DiscreteGeometry_Kourimska.pdf
  file_size: 1026683
  relation: main_file
  success: 1
file_date_updated: 2023-10-04T11:46:24Z
has_accepted_license: '1'
intvolume: '        70'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 123-153
pmid: 1
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I04245
  name: Algebraic Footprints of Geometric Features in Homology
publication: Discrete and Computational Geometry
publication_identifier:
  eissn:
  - 1432-0444
  issn:
  - 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Discrete yamabe problem for polyhedral surfaces
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 70
year: '2023'
...