{"id":"https://openalex.org/W4411169750","doi":"https://doi.org/10.1007/s00454-025-00749-y","title":"Decorated Discrete Conformal Equivalence in Non-Euclidean Geometries","display_name":"Decorated Discrete Conformal Equivalence in Non-Euclidean Geometries","publication_year":2025,"publication_date":"2025-06-10","ids":{"openalex":"https://openalex.org/W4411169750","doi":"https://doi.org/10.1007/s00454-025-00749-y"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-025-00749-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00749-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00749-y.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00749-y.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109493283","display_name":"Alexander I. Bobenko","orcid":"https://orcid.org/0009-0008-0954-043X"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alexander I. Bobenko","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Str. des 17. Juni 136, 10623, Berlin, Germany"],"raw_orcid":"https://orcid.org/0009-0008-0954-043X","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Str. des 17. Juni 136, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088587531","display_name":"Carl O. R. Lutz","orcid":"https://orcid.org/0000-0003-2533-873X"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Carl O. R. Lutz","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Str. des 17. Juni 136, 10623, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Str. des 17. Juni 136, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109493283"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":2.4764,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.85381808,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"76","issue":"1","first_page":"416","last_page":"465"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conformal-map","display_name":"Conformal map","score":0.7557848691940308},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6916472911834717},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6053270697593689},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5014615058898926},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4336755573749542},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3474186360836029}],"concepts":[{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.7557848691940308},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6916472911834717},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6053270697593689},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5014615058898926},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4336755573749542},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3474186360836029}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-025-00749-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00749-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00749-y.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00454-025-00749-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00749-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00749-y.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G822936381","display_name":"TRR 109: Diskretisierung in Geometrie und Dynamik","funder_award_id":"195170736","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8703222197","display_name":null,"funder_award_id":"SFB/TRR109","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8876951107","display_name":null,"funder_award_id":"TRR109","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320324094","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411169750.pdf","grobid_xml":"https://content.openalex.org/works/W4411169750.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W1511400044","https://openalex.org/W1525548751","https://openalex.org/W1536497458","https://openalex.org/W1547598092","https://openalex.org/W1568457649","https://openalex.org/W1631732175","https://openalex.org/W1784898840","https://openalex.org/W1966231024","https://openalex.org/W1970334962","https://openalex.org/W1974956622","https://openalex.org/W1989283616","https://openalex.org/W2029351091","https://openalex.org/W2040020758","https://openalex.org/W2048041714","https://openalex.org/W2077265709","https://openalex.org/W2096951306","https://openalex.org/W2136126748","https://openalex.org/W2144485551","https://openalex.org/W2163787581","https://openalex.org/W2312447353","https://openalex.org/W2508233477","https://openalex.org/W2614944118","https://openalex.org/W2962889517","https://openalex.org/W2963610207","https://openalex.org/W2963925837","https://openalex.org/W2972073756","https://openalex.org/W3000918815","https://openalex.org/W3103304244","https://openalex.org/W3121172951","https://openalex.org/W3202969107","https://openalex.org/W4205113243","https://openalex.org/W4205986227","https://openalex.org/W4229576119","https://openalex.org/W4247349089","https://openalex.org/W4248866312","https://openalex.org/W4254306788","https://openalex.org/W4254697999","https://openalex.org/W4292166790","https://openalex.org/W4360980667","https://openalex.org/W4389426508","https://openalex.org/W4393714693"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2747077871","https://openalex.org/W1971223889","https://openalex.org/W2173406670","https://openalex.org/W2085963144","https://openalex.org/W2011016219","https://openalex.org/W2392707140","https://openalex.org/W805371022","https://openalex.org/W4256250254","https://openalex.org/W1506630056"],"abstract_inverted_index":{"Abstract":[0],"We":[1,61,91],"introduce":[2,82],"decorated":[3,29,55,99],"piecewise":[4,56,100],"hyperbolic":[5,42,45,57],"and":[6,9,44,58,103,128],"spherical":[7,59,104],"surfaces":[8,30,105],"discuss":[10],"their":[11],"discrete":[12,88,126],"conformal":[13,48,89],"equivalence.":[14],"A":[15],"decoration":[16],"is":[17,71,112],"a":[18,72,76,83,115,121],"choice":[19],"of":[20,25,41],"circle":[21,37],"about":[22],"each":[23,67],"vertex":[24],"the":[26,63,87,107,125],"surface.":[27,79],"Our":[28,110],"are":[31],"closely":[32],"related":[33],"to":[34,123],"inversive":[35],"distance":[36],"packings,":[38],"canonical":[39],"tessellations":[40],"surfaces,":[43],"polyhedra.":[46],"Discrete":[47],"equivalence":[49,52,68],"introduces":[50],"an":[51],"relation":[53],"on":[54,75,114],"surfaces.":[60],"prove":[62],"corresponding":[64],"uniformization":[65,127],"theorem\u2014in":[66],"class":[69],"there":[70],"unique":[73],"representative":[74],"constant":[77],"curvature":[78],"Furthermore,":[80],"we":[81],"fundamental":[84],"invariant":[85],"characterizing":[86],"classes.":[90],"show":[92],"that":[93],"one":[94],"can":[95],"deform":[96],"continuously":[97],"between":[98],"hyperbolic,":[101],"Euclidean,":[102],"sharing":[106],"same":[108],"invariant.":[109],"approach":[111],"based":[113],"variational":[116],"principle,":[117],"which":[118],"also":[119],"provides":[120],"way":[122],"compute":[124],"geometric":[129],"transitions.":[130]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}