{"id":"https://openalex.org/W2116672578","doi":"https://doi.org/10.1112/s1461157000001170","title":"A Bound on the Number of Endpoints of the Cut Locus","display_name":"A Bound on the Number of Endpoints of the Cut Locus","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2116672578","doi":"https://doi.org/10.1112/s1461157000001170","mag":"2116672578"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157000001170","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000001170","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1BAE11FC9C1BBF30E99D9FAA5CB50EA8/S1461157000001170a.pdf/div-class-title-a-bound-on-the-number-of-endpoints-of-the-cut-locus-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1BAE11FC9C1BBF30E99D9FAA5CB50EA8/S1461157000001170a.pdf/div-class-title-a-bound-on-the-number-of-endpoints-of-the-cut-locus-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071082834","display_name":"Robert Sinclair","orcid":"https://orcid.org/0000-0002-9646-4322"},"institutions":[{"id":"https://openalex.org/I32915989","display_name":"University of the Ryukyus","ror":"https://ror.org/02z1n9q24","country_code":"JP","type":"education","lineage":["https://openalex.org/I32915989"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Robert Sinclair","raw_affiliation_strings":["Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus, Nishihara City, Okinawa 903\u20130213, Japan","Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus, Nishihara City, Okinawa 903\u20130213, Japan, sinclair@math.u-ryukyu.ac.jp, http/homepage.mac.com/r_m_sinclair"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus, Nishihara City, Okinawa 903\u20130213, Japan","institution_ids":["https://openalex.org/I32915989"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus, Nishihara City, Okinawa 903\u20130213, Japan, sinclair@math.u-ryukyu.ac.jp, http/homepage.mac.com/r_m_sinclair","institution_ids":["https://openalex.org/I32915989"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001899038","display_name":"Minoru Tanaka","orcid":"https://orcid.org/0000-0002-7009-7851"},"institutions":[{"id":"https://openalex.org/I1314466530","display_name":"Tokai University","ror":"https://ror.org/01p7qe739","country_code":"JP","type":"education","lineage":["https://openalex.org/I1314466530"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Minoru Tanaka","raw_affiliation_strings":["Department of Mathematics, Tokai University, Hiratsuka City, Kanagawa 259\u20131292, Japan","Department of Mathematics, Tokai University, Hiratsuka City, Kanagawa 259\u20131292, Japan, m-tanaka@sm.u-tokai.ac.jp"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tokai University, Hiratsuka City, Kanagawa 259\u20131292, Japan","institution_ids":["https://openalex.org/I1314466530"]},{"raw_affiliation_string":"Department of Mathematics, Tokai University, Hiratsuka City, Kanagawa 259\u20131292, Japan, m-tanaka@sm.u-tokai.ac.jp","institution_ids":["https://openalex.org/I1314466530"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4375,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.74897119,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"9","issue":null,"first_page":"21","last_page":"39"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9868000149726868,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8695192337036133},{"id":"https://openalex.org/keywords/locus","display_name":"Locus (genetics)","score":0.6790328025817871},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6626958250999451},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6150707006454468},{"id":"https://openalex.org/keywords/cut-point","display_name":"Cut-point","score":0.5645883083343506},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5146811604499817},{"id":"https://openalex.org/keywords/gaussian-curvature","display_name":"Gaussian curvature","score":0.4674055874347687},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4353688061237335},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.3383680582046509},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.31890758872032166},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28162050247192383},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19723856449127197}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8695192337036133},{"id":"https://openalex.org/C84597430","wikidata":"https://www.wikidata.org/wiki/Q106227","display_name":"Locus (genetics)","level":3,"score":0.6790328025817871},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6626958250999451},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6150707006454468},{"id":"https://openalex.org/C2781415353","wikidata":"https://www.wikidata.org/wiki/Q5196602","display_name":"Cut-point","level":2,"score":0.5645883083343506},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5146811604499817},{"id":"https://openalex.org/C16140857","wikidata":"https://www.wikidata.org/wiki/Q945953","display_name":"Gaussian curvature","level":3,"score":0.4674055874347687},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4353688061237335},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.3383680582046509},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.31890758872032166},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28162050247192383},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19723856449127197},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1112/s1461157000001170","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000001170","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1BAE11FC9C1BBF30E99D9FAA5CB50EA8/S1461157000001170a.pdf/div-class-title-a-bound-on-the-number-of-endpoints-of-the-cut-locus-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1112/s1461157000001170","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000001170","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1BAE11FC9C1BBF30E99D9FAA5CB50EA8/S1461157000001170a.pdf/div-class-title-a-bound-on-the-number-of-endpoints-of-the-cut-locus-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2116672578.pdf","grobid_xml":"https://content.openalex.org/works/W2116672578.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W262419327","https://openalex.org/W603049876","https://openalex.org/W604719300","https://openalex.org/W1485657194","https://openalex.org/W1507810258","https://openalex.org/W1525133530","https://openalex.org/W1557110756","https://openalex.org/W1572115049","https://openalex.org/W1664360780","https://openalex.org/W1973179349","https://openalex.org/W1977044533","https://openalex.org/W1981220214","https://openalex.org/W2000129712","https://openalex.org/W2025135786","https://openalex.org/W2037876304","https://openalex.org/W2037899862","https://openalex.org/W2045438304","https://openalex.org/W2057687829","https://openalex.org/W2065087331","https://openalex.org/W2083327141","https://openalex.org/W2091141455","https://openalex.org/W2321230360","https://openalex.org/W2322920544","https://openalex.org/W2333982333","https://openalex.org/W2494377738","https://openalex.org/W3004076791","https://openalex.org/W3040283615","https://openalex.org/W4230646996","https://openalex.org/W4234121922","https://openalex.org/W4242926628","https://openalex.org/W4247528458","https://openalex.org/W6634213782","https://openalex.org/W6662023582","https://openalex.org/W6780347575"],"related_works":["https://openalex.org/W4295655570","https://openalex.org/W4308065694","https://openalex.org/W2951720092","https://openalex.org/W4226297850","https://openalex.org/W846690687","https://openalex.org/W2079841776","https://openalex.org/W73664651","https://openalex.org/W2504596514","https://openalex.org/W4321101434","https://openalex.org/W3215570221"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"provide":[2],"strong":[3],"experimental":[4],"evidence":[5],"for":[6],"an":[7],"upper":[8],"bound":[9,28],"on":[10,22],"the":[11,16,32,51],"number":[12,34],"of":[13,15,25,35,37],"endpoints":[14],"cut":[17],"locus":[18],"from":[19,47],"a":[20,23],"point":[21],"2-surface":[24],"revolution.":[26],"This":[27],"is":[29],"equal":[30],"to":[31,50],"minimal":[33],"intervals":[36],"monotone":[38],"non-increasing":[39],"or":[40],"non-decreasing":[41],"Gaussian":[42],"curvature":[43],"along":[44],"one":[45,48],"meridian":[46],"pole":[49],"other.":[52]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
