{"id":"https://openalex.org/W2024908347","doi":"https://doi.org/10.4007/annals.2008.167.1079","title":"Manifolds with positive curvature operators are space forms","display_name":"Manifolds with positive curvature operators are space forms","publication_year":2008,"publication_date":"2008-05-01","ids":{"openalex":"https://openalex.org/W2024908347","doi":"https://doi.org/10.4007/annals.2008.167.1079","mag":"2024908347"},"language":"en","primary_location":{"id":"doi:10.4007/annals.2008.167.1079","doi":"https://doi.org/10.4007/annals.2008.167.1079","is_oa":true,"landing_page_url":"https://doi.org/10.4007/annals.2008.167.1079","pdf_url":"http://annals.math.princeton.edu/wp-content/uploads/annals-v167-n3-p10.pdf","source":{"id":"https://openalex.org/S45918994","display_name":"Annals of Mathematics","issn_l":"0003-486X","issn":["0003-486X","1939-8980"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310316273","host_organization_name":"Princeton University","host_organization_lineage":["https://openalex.org/P4310316273"],"host_organization_lineage_names":["Princeton University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2024908347"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"http://annals.math.princeton.edu/wp-content/uploads/annals-v167-n3-p10.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078432598","display_name":"Christoph B\u00f6hm","orcid":"https://orcid.org/0000-0001-9681-1382","observed_orcids":["https://orcid.org/0000-0001-9681-1382"]},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christoph B\u00f6hm","raw_affiliation_strings":["Mathematical Institute<br/>University of M\u00fcnster<br/>D-48149 M\u00fcnster<br/>Germany","Mathematical Institute University of M\u00fcnster D-48149 M\u00fcnster Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute<br/>University of M\u00fcnster<br/>D-48149 M\u00fcnster<br/>Germany","institution_ids":["https://openalex.org/I22465464"]},{"raw_affiliation_string":"Mathematical Institute University of M\u00fcnster D-48149 M\u00fcnster Germany","institution_ids":["https://openalex.org/I22465464"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003751709","display_name":"Burkhard Wilking","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Burkhard Wilking","raw_affiliation_strings":["Mathematical Institute<br/>University of M\u00fcnster<br/>D-48149 M\u00fcnster<br/>Germany","Mathematical Institute University of M\u00fcnster D-48149 M\u00fcnster Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute<br/>University of M\u00fcnster<br/>D-48149 M\u00fcnster<br/>Germany","institution_ids":["https://openalex.org/I22465464"]},{"raw_affiliation_string":"Mathematical Institute University of M\u00fcnster D-48149 M\u00fcnster Germany","institution_ids":["https://openalex.org/I22465464"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I22465464"],"apc_list":null,"apc_paid":null,"fwci":23.0616,"has_fulltext":true,"cited_by_count":290,"citation_normalized_percentile":{"value":0.99900258,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"167","issue":"3","first_page":"1079","last_page":"1097"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9965999722480774,"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":0.9965999722480774,"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":0.001500000013038516,"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/T12351","display_name":"Geometry and complex manifolds","score":0.00139999995008111,"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/space-forms","display_name":"space forms","score":0.9599999785423279},{"id":"https://openalex.org/keywords/normalized-ricci-flow","display_name":"normalized Ricci flow","score":0.9359999895095825},{"id":"https://openalex.org/keywords/constant-curvature-metrics","display_name":"constant curvature metrics","score":0.746999979019165},{"id":"https://openalex.org/keywords/compact-manifolds","display_name":"compact manifolds","score":0.9210000038146973},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.609000027179718}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8815007209777832},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.6285412311553955},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6118214130401611},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.610568642616272},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.610047459602356},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5686551332473755},{"id":"https://openalex.org/C148729565","wikidata":"https://www.wikidata.org/wiki/Q1361396","display_name":"Ricci flow","level":4,"score":0.5527434349060059},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5422587394714355},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.5038248896598816},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.48059985041618347},{"id":"https://openalex.org/C183517385","wikidata":"https://www.wikidata.org/wiki/Q855112","display_name":"Riemann curvature tensor","level":3,"score":0.4519977569580078},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.44319936633110046},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1649777591228485},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.4007/annals.2008.167.1079","doi":"https://doi.org/10.4007/annals.2008.167.1079","is_oa":true,"landing_page_url":"https://doi.org/10.4007/annals.2008.167.1079","pdf_url":"http://annals.math.princeton.edu/wp-content/uploads/annals-v167-n3-p10.pdf","source":{"id":"https://openalex.org/S45918994","display_name":"Annals of Mathematics","issn_l":"0003-486X","issn":["0003-486X","1939-8980"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310316273","host_organization_name":"Princeton University","host_organization_lineage":["https://openalex.org/P4310316273"],"host_organization_lineage_names":["Princeton University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0606187","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0606187","pdf_url":"https://arxiv.org/pdf/math/0606187","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.math/0606187","doi":"https://doi.org/10.48550/arxiv.math/0606187","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.math/0606187","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.142.3869","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.142.3869","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://annals.math.princeton.edu/issues/2007/FinalFiles/BoehmWilkingFinal.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.4007/annals.2008.167.1079","doi":"https://doi.org/10.4007/annals.2008.167.1079","is_oa":true,"landing_page_url":"https://doi.org/10.4007/annals.2008.167.1079","pdf_url":"http://annals.math.princeton.edu/wp-content/uploads/annals-v167-n3-p10.pdf","source":{"id":"https://openalex.org/S45918994","display_name":"Annals of Mathematics","issn_l":"0003-486X","issn":["0003-486X","1939-8980"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310316273","host_organization_name":"Princeton University","host_organization_lineage":["https://openalex.org/P4310316273"],"host_organization_lineage_names":["Princeton University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2024908347.pdf","grobid_xml":"https://content.openalex.org/works/W2024908347.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W62340590","https://openalex.org/W1505438101","https://openalex.org/W1509364003","https://openalex.org/W1530161281","https://openalex.org/W1574024211","https://openalex.org/W1587723526","https://openalex.org/W1598234271","https://openalex.org/W1611092396","https://openalex.org/W1970564715","https://openalex.org/W1972386875","https://openalex.org/W1978899451","https://openalex.org/W2030221916","https://openalex.org/W2033250281","https://openalex.org/W2034032542","https://openalex.org/W2082185881","https://openalex.org/W2083027035","https://openalex.org/W2094306368","https://openalex.org/W2963816048","https://openalex.org/W3138701353","https://openalex.org/W6603777891","https://openalex.org/W6605693289","https://openalex.org/W6606275768","https://openalex.org/W6638407004","https://openalex.org/W6639206960"],"related_works":["https://openalex.org/W4294904682","https://openalex.org/W2158350859","https://openalex.org/W2963654695","https://openalex.org/W2964178396","https://openalex.org/W4315762337","https://openalex.org/W1978685440","https://openalex.org/W2012648446","https://openalex.org/W2066221527","https://openalex.org/W7223004070"],"abstract_inverted_index":{"We":[0],"confirm":[1],"a":[2],"conjecture":[3],"of":[4],"Hamilton:":[5],"On":[6],"compact":[7],"manifolds":[8],"the":[9],"normalized":[10],"Ricci":[11],"flow":[12],"evolves":[13],"metrics":[14,21],"with":[15,22],"positive":[16],"curvature":[17],"operators":[18],"to":[19],"limit":[20],"constant":[23],"curvature.":[24]},"counts_by_year":[{"year":2026,"cited_by_count":18},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":18},{"year":2013,"cited_by_count":22},{"year":2012,"cited_by_count":16}],"updated_date":"2026-11-15T12:55:33.944570","created_date":"2016-06-24T00:00:00"}
