{"id":"https://openalex.org/W1983128233","doi":"https://doi.org/10.1007/s12220-011-9260-6","title":"Bifurcation of Constant Mean Curvature Tori in Euclidean Spheres","display_name":"Bifurcation of Constant Mean Curvature Tori in Euclidean Spheres","publication_year":2011,"publication_date":"2011-09-22","ids":{"openalex":"https://openalex.org/W1983128233","doi":"https://doi.org/10.1007/s12220-011-9260-6","mag":"1983128233"},"language":"en","primary_location":{"id":"doi:10.1007/s12220-011-9260-6","doi":"https://doi.org/10.1007/s12220-011-9260-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12220-011-9260-6","pdf_url":null,"source":{"id":"https://openalex.org/S6775291","display_name":"Journal of Geometric Analysis","issn_l":"1050-6926","issn":["1050-6926","1559-002X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-2","norway-2","poland-100","russia-white-list-2","vabb-shw"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Geometric Analysis","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001698570","display_name":"Luis J. Al\u0131\u0301as","orcid":"https://orcid.org/0000-0002-8482-4888","observed_orcids":["https://orcid.org/0000-0002-8482-4888"]},"institutions":[{"id":"https://openalex.org/I80180929","display_name":"Universidad de Murcia","ror":"https://ror.org/03p3aeb86","country_code":"ES","type":"education","lineage":["https://openalex.org/I80180929"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Luis J. Al\u00edas","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad de Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain","Departamento de Matem\u00e1ticas, Universidad de Murcia, Espinardo, Spain","UNIVERSIDAD DE MURCIA ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain","institution_ids":["https://openalex.org/I80180929"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Murcia, Espinardo, Spain","institution_ids":["https://openalex.org/I80180929"]},{"raw_affiliation_string":"UNIVERSIDAD DE MURCIA ,","institution_ids":["https://openalex.org/I80180929"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Luis J. Al\u00edas","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]},{"id":"https://openalex.org/I80180929","display_name":"Universidad de Murcia","ror":"https://ror.org/03p3aeb86","country_code":"ES","type":"education","lineage":["https://openalex.org/I80180929"]}],"countries":["BR","ES"],"is_corresponding":false,"raw_author_name":"Luis J. Al\u00edas","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad de Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain","Departamento de Matem\u00e1ticas, Universidad de Murcia, Espinardo, Spain","Universidad de Murcia","Universidade de S\u00e3o Paulo"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain","institution_ids":["https://openalex.org/I80180929"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Murcia, Espinardo, Spain","institution_ids":["https://openalex.org/I80180929"]},{"raw_affiliation_string":"Universidad de Murcia","institution_ids":["https://openalex.org/I80180929"]},{"raw_affiliation_string":"Universidade de S\u00e3o Paulo","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049749113","display_name":"Paolo Piccione","orcid":"https://orcid.org/0000-0002-8929-5938","observed_orcids":["https://orcid.org/0000-0002-8929-5938"]},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]},{"id":"https://openalex.org/I80180929","display_name":"Universidad de Murcia","ror":"https://ror.org/03p3aeb86","country_code":"ES","type":"education","lineage":["https://openalex.org/I80180929"]}],"countries":["BR","ES"],"is_corresponding":false,"raw_author_name":"Paolo Piccione","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Universidade de S\u00e3o Paulo, Rua do Mat\u00e3o 1010, CEP 05508-900, S\u00e3o Paulo, SP, Brazil","Departamento de Matem\u00e1tica, Universidade de S\u00e3o Paulo, S\u00e3o Paulo, Brazil","Departamento de Matem\u00e1ticas, Universidad de Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain","Departamento de Matem\u00e1ticas, Universidad de Murcia, Espinardo, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade de S\u00e3o Paulo, Rua do Mat\u00e3o 1010, CEP 05508-900, S\u00e3o Paulo, SP, Brazil","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade de S\u00e3o Paulo, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain","institution_ids":["https://openalex.org/I80180929"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Murcia, Espinardo, Spain","institution_ids":["https://openalex.org/I80180929"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049749113","display_name":"Paolo Piccione","orcid":"https://orcid.org/0000-0002-8929-5938","observed_orcids":["https://orcid.org/0000-0002-8929-5938"]},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]},{"id":"https://openalex.org/I80180929","display_name":"Universidad de Murcia","ror":"https://ror.org/03p3aeb86","country_code":"ES","type":"education","lineage":["https://openalex.org/I80180929"]}],"countries":["BR","ES"],"is_corresponding":true,"raw_author_name":"Paolo Piccione","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Universidade de S\u00e3o Paulo, Rua do Mat\u00e3o 1010, CEP 05508-900, S\u00e3o Paulo, SP, Brazil","Departamento de Matem\u00e1tica, Universidade de S\u00e3o Paulo, S\u00e3o Paulo, Brazil","Departamento de Matem\u00e1ticas, Universidad de Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain","Departamento de Matem\u00e1ticas, Universidad de Murcia, Espinardo, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade de S\u00e3o Paulo, Rua do Mat\u00e3o 1010, CEP 05508-900, S\u00e3o Paulo, SP, Brazil","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade de S\u00e3o Paulo, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain","institution_ids":["https://openalex.org/I80180929"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Murcia, Espinardo, Spain","institution_ids":["https://openalex.org/I80180929"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001698570","https://openalex.org/A5049749113"],"corresponding_institution_ids":["https://openalex.org/I17974374","https://openalex.org/I80180929"],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":null,"fwci":3.1589,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.89926532,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"23","issue":"2","first_page":"677","last_page":"708"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9916999936103821,"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":0.9916999936103821,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.0066999997943639755,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.00039999998989515007,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/constant-mean-curvature","display_name":"constant mean curvature","score":0.8709999918937683},{"id":"https://openalex.org/keywords/euclidean-sphere","display_name":"Euclidean sphere","score":0.8790000081062317},{"id":"https://openalex.org/keywords/equivariant-bifurcation-theory","display_name":"equivariant bifurcation theory","score":0.9020000100135803},{"id":"https://openalex.org/keywords/isometric-embedding","display_name":"isometric embedding","score":0.9350000023841858},{"id":"https://openalex.org/keywords/clifford-torus","display_name":"Clifford torus","score":0.9139999747276306}],"concepts":[{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.8119044899940491},{"id":"https://openalex.org/C56402544","wikidata":"https://www.wikidata.org/wiki/Q5133090","display_name":"Clifford torus","level":3,"score":0.7727848291397095},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.6935043334960938},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.6841205954551697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6659496426582336},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6350173354148865},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.628572404384613},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.5623750686645508},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5205560326576233},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5075172185897827},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4643803834915161},{"id":"https://openalex.org/C2779668893","wikidata":"https://www.wikidata.org/wiki/Q2250422","display_name":"Constant curvature","level":3,"score":0.4542354941368103},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43738672137260437},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27507856488227844},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24516692757606506},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07170233130455017},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.058464497327804565},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.058177173137664795},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12220-011-9260-6","doi":"https://doi.org/10.1007/s12220-011-9260-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12220-011-9260-6","pdf_url":null,"source":{"id":"https://openalex.org/S6775291","display_name":"Journal of Geometric Analysis","issn_l":"1050-6926","issn":["1050-6926","1559-002X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-2","norway-2","poland-100","russia-white-list-2","vabb-shw"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Geometric Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W144774350","https://openalex.org/W615662743","https://openalex.org/W1492844808","https://openalex.org/W1514801494","https://openalex.org/W1515066108","https://openalex.org/W1531608165","https://openalex.org/W1578397986","https://openalex.org/W1578739045","https://openalex.org/W1611618725","https://openalex.org/W1866311589","https://openalex.org/W1975006901","https://openalex.org/W1986848299","https://openalex.org/W1990044088","https://openalex.org/W1994445715","https://openalex.org/W1995483478","https://openalex.org/W2011950750","https://openalex.org/W2012789921","https://openalex.org/W2018063028","https://openalex.org/W2023861252","https://openalex.org/W2026294216","https://openalex.org/W2026386044","https://openalex.org/W2038829320","https://openalex.org/W2059256389","https://openalex.org/W2070166786","https://openalex.org/W2071788826","https://openalex.org/W2078708427","https://openalex.org/W2083998303","https://openalex.org/W2085222282","https://openalex.org/W2092696532","https://openalex.org/W2097889043","https://openalex.org/W2125507914","https://openalex.org/W2128911695","https://openalex.org/W2160303068","https://openalex.org/W2264990502","https://openalex.org/W2368936679","https://openalex.org/W2729975235","https://openalex.org/W2794435666","https://openalex.org/W2898348186","https://openalex.org/W2962822546","https://openalex.org/W2998340964","https://openalex.org/W3037337287","https://openalex.org/W4233424473","https://openalex.org/W4238037803","https://openalex.org/W4238203073","https://openalex.org/W4243429967","https://openalex.org/W4251031601","https://openalex.org/W4302394292","https://openalex.org/W6630276469"],"related_works":["https://openalex.org/W1634687674","https://openalex.org/W2951057104","https://openalex.org/W4389469227","https://openalex.org/W4324143904","https://openalex.org/W2791033474","https://openalex.org/W1545882520","https://openalex.org/W3134115586","https://openalex.org/W4225647094","https://openalex.org/W4297936111","https://openalex.org/W1566793283"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-10-23T09:35:12.469056","created_date":"2025-10-10T00:00:00"}