{"id":"https://openalex.org/W1481230041","doi":"https://doi.org/10.1007/11537908_9","title":"Level Sets of Functions and Symmetry Sets of Surface Sections","display_name":"Level Sets of Functions and Symmetry Sets of Surface Sections","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1481230041","doi":"https://doi.org/10.1007/11537908_9","mag":"1481230041"},"language":"en","primary_location":{"id":"doi:10.1007/11537908_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11537908_9","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0504393","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104607841","display_name":"Andr\u00e9 Diatta","orcid":"https://orcid.org/0000-0001-9435-750X"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Andr\u00e9 Diatta","raw_affiliation_strings":["University of Liverpool, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110431325","display_name":"Peter Giblin","orcid":null},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Peter Giblin","raw_affiliation_strings":["University of Liverpool, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053392094","display_name":"Brendan Guilfoyle","orcid":"https://orcid.org/0000-0002-7437-5046"},"institutions":[{"id":"https://openalex.org/I4210100923","display_name":"Munster Technological University","ror":"https://ror.org/013xpqh61","country_code":"IE","type":"facility","lineage":["https://openalex.org/I4210100923"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Brendan Guilfoyle","raw_affiliation_strings":["Institute of Technology, Tralee, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Technology, Tralee, Ireland","institution_ids":["https://openalex.org/I4210100923"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072445764","display_name":"Wilhelm Klingenberg","orcid":"https://orcid.org/0000-0001-7876-579X"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Wilhelm Klingenberg","raw_affiliation_strings":["University of Durham, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Durham, UK","institution_ids":["https://openalex.org/I190082696"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.1915,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.87825059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"147","last_page":"160"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9876000285148621,"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"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9876000285148621,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9855999946594238,"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"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9846000075340271,"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/smoothness","display_name":"Smoothness","score":0.6970807313919067},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6426565647125244},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.6090026497840881},{"id":"https://openalex.org/keywords/cusp","display_name":"Cusp (singularity)","score":0.5930344462394714},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5880955457687378},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.5493764281272888},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5356893539428711},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5154691338539124},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5002846717834473},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49840617179870605},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4887216091156006},{"id":"https://openalex.org/keywords/section","display_name":"Section (typography)","score":0.46353650093078613},{"id":"https://openalex.org/keywords/parametric-surface","display_name":"Parametric surface","score":0.4507664144039154},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4478510320186615},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43502259254455566},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4237968325614929},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.42228615283966064},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41996943950653076},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3244314193725586},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.26788973808288574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2021477222442627},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19189268350601196},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06815943121910095}],"concepts":[{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6970807313919067},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6426565647125244},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.6090026497840881},{"id":"https://openalex.org/C2778400075","wikidata":"https://www.wikidata.org/wiki/Q655275","display_name":"Cusp (singularity)","level":2,"score":0.5930344462394714},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5880955457687378},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5493764281272888},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5356893539428711},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5154691338539124},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5002846717834473},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49840617179870605},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4887216091156006},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.46353650093078613},{"id":"https://openalex.org/C2187777","wikidata":"https://www.wikidata.org/wiki/Q1071743","display_name":"Parametric surface","level":3,"score":0.4507664144039154},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4478510320186615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43502259254455566},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4237968325614929},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.42228615283966064},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41996943950653076},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3244314193725586},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.26788973808288574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2021477222442627},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19189268350601196},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06815943121910095},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/11537908_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11537908_9","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:arXiv.org:math/0504393","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0504393","pdf_url":"https://arxiv.org/pdf/math/0504393","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:durham-repository.worktribe.com:1162779","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/output/1162779","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Presentation / Conference Contribution"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0504393","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0504393","pdf_url":"https://arxiv.org/pdf/math/0504393","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W339295896","https://openalex.org/W1497235707","https://openalex.org/W1502571467","https://openalex.org/W1553756388","https://openalex.org/W1964206745","https://openalex.org/W1989389927","https://openalex.org/W2077931785","https://openalex.org/W2093793201","https://openalex.org/W2496526329","https://openalex.org/W2611234013","https://openalex.org/W2740373864","https://openalex.org/W2970425058","https://openalex.org/W3104563367"],"related_works":["https://openalex.org/W2587346990","https://openalex.org/W2417802712","https://openalex.org/W2026692681","https://openalex.org/W2393022482","https://openalex.org/W2377346130","https://openalex.org/W2361092061","https://openalex.org/W1631792327","https://openalex.org/W3122961362","https://openalex.org/W4289545316","https://openalex.org/W3142835046"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2016-06-24T00:00:00"}