{"id":"https://openalex.org/W1969836943","doi":"https://doi.org/10.1112/jlms/jdt014","title":"Complex intersection bodies","display_name":"Complex intersection bodies","publication_year":2013,"publication_date":"2013-08-16","ids":{"openalex":"https://openalex.org/W1969836943","doi":"https://doi.org/10.1112/jlms/jdt014","mag":"1969836943"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdt014","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdt014","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1201.0437","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102833837","display_name":"Alexander Koldobsky","orcid":"https://orcid.org/0000-0002-9963-1894"},"institutions":[{"id":"https://openalex.org/I76835614","display_name":"University of Missouri","ror":"https://ror.org/02ymw8z06","country_code":"US","type":"education","lineage":["https://openalex.org/I76835614"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Koldobsky","raw_affiliation_strings":["Department of Mathematics, University of Missouri, Columbia, MO 65211, USA, [email protected]","Department of Mathematics, University of Missouri, Columbia, MO 65211, USA, koldobskiya@missouri.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Missouri, Columbia, MO 65211, USA, [email protected]","institution_ids":["https://openalex.org/I76835614"]},{"raw_affiliation_string":"Department of Mathematics, University of Missouri, Columbia, MO 65211, USA, koldobskiya@missouri.edu","institution_ids":["https://openalex.org/I76835614"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057513793","display_name":"Grigoris Paouris","orcid":"https://orcid.org/0000-0002-2619-0207"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G. Paouris","raw_affiliation_strings":["Department of Mathematics, Texas A & M University, College Station, TX 77843-3368, USA, [email protected]","Department of Mathematics, Texas A & M University, College Station, TX 77843-3368, USA, grigoris@math.tamu.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A & M University, College Station, TX 77843-3368, USA, [email protected]","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Mathematics, Texas A & M University, College Station, TX 77843-3368, USA, grigoris@math.tamu.edu","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045301740","display_name":"Marisa Zymonopoulou","orcid":"https://orcid.org/0000-0002-9732-8920"},"institutions":[{"id":"https://openalex.org/I142617266","display_name":"University of Crete","ror":"https://ror.org/00dr28g20","country_code":"GR","type":"education","lineage":["https://openalex.org/I142617266"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"M. Zymonopoulou","raw_affiliation_strings":["Department of Mathematics, University of Crete, PO Box 2208, Iraklio, 71409 Crete, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Crete, PO Box 2208, Iraklio, 71409 Crete, Greece","institution_ids":["https://openalex.org/I142617266"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045301740"],"corresponding_institution_ids":["https://openalex.org/I142617266"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":7.5802,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.97624873,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"88","issue":"2","first_page":"538","last_page":"562"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9998000264167786,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9998000264167786,"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/intersection","display_name":"Intersection (aeronautics)","score":0.8866440057754517},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.7934911251068115},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5825026035308838},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5467220544815063},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3991321623325348},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3357999324798584},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19716909527778625},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.0955275297164917},{"id":"https://openalex.org/keywords/cartography","display_name":"Cartography","score":0.0649334192276001}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.8866440057754517},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.7934911251068115},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5825026035308838},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5467220544815063},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3991321623325348},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3357999324798584},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19716909527778625},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0955275297164917},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0649334192276001}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1112/jlms/jdt014","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdt014","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1201.0437","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1201.0437","pdf_url":"https://arxiv.org/pdf/1201.0437","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:CiteSeerX.psu:10.1.1.296.538","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.296.538","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.missouri.edu/~koldobsk/complex-int-final.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.761.7140","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.761.7140","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1201.0437.pdf","raw_type":"text"},{"id":"pmh:oai:circle.library.ubc.ca:2429/49523","is_oa":true,"landing_page_url":"http://hdl.handle.net/2429/49523","pdf_url":null,"source":{"id":"https://openalex.org/S4377196297","display_name":"cIRcle (University of British Columbia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I141945490","host_organization_name":"University of British Columbia","host_organization_lineage":["https://openalex.org/I141945490"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Moving Image"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1201.0437","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1201.0437","pdf_url":"https://arxiv.org/pdf/1201.0437","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":[{"score":0.4300000071525574,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W615000568","https://openalex.org/W638923023","https://openalex.org/W644522774","https://openalex.org/W1521305480","https://openalex.org/W1571966798","https://openalex.org/W1604027237","https://openalex.org/W1970476235","https://openalex.org/W1971692071","https://openalex.org/W1984024149","https://openalex.org/W1989796976","https://openalex.org/W2004501929","https://openalex.org/W2005553961","https://openalex.org/W2006252618","https://openalex.org/W2017008566","https://openalex.org/W2028299436","https://openalex.org/W2039486702","https://openalex.org/W2041032149","https://openalex.org/W2041222127","https://openalex.org/W2041947933","https://openalex.org/W2042124498","https://openalex.org/W2044246986","https://openalex.org/W2046841627","https://openalex.org/W2059033534","https://openalex.org/W2059748356","https://openalex.org/W2069428056","https://openalex.org/W2071303594","https://openalex.org/W2073912709","https://openalex.org/W2076183396","https://openalex.org/W2079483320","https://openalex.org/W2084183060","https://openalex.org/W2084878648","https://openalex.org/W2087867172","https://openalex.org/W2087964196","https://openalex.org/W2141935810","https://openalex.org/W2161630387","https://openalex.org/W4234625385","https://openalex.org/W4241397713","https://openalex.org/W4246483361","https://openalex.org/W4253558876","https://openalex.org/W4254502176"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2369655046","https://openalex.org/W2019467317","https://openalex.org/W1585519779","https://openalex.org/W1965515989","https://openalex.org/W2088737283","https://openalex.org/W1999587863","https://openalex.org/W1929902734","https://openalex.org/W4376167435","https://openalex.org/W2042783797"],"abstract_inverted_index":{"We":[0],"introduce":[1],"complex":[2,28,33,38,50,64],"intersection":[3,34,65],"bodies":[4,35,40],"and":[5,10,56],"show":[6],"that":[7,32],"their":[8,17],"properties":[9],"applications":[11],"are":[12,41],"similar":[13],"to":[14,26],"those":[15],"of":[16,36,63],"real":[18],"counterparts.":[19],"In":[20],"particular,":[21],"we":[22],"generalize":[23],"Busemann's":[24],"theorem":[25],"the":[27,49,57],"case":[29],"by":[30],"proving":[31],"symmetric":[37],"convex":[39],"also":[42],"convex.":[43],"Other":[44],"results":[45],"include":[46],"stability":[47],"in":[48],"Busemann\u2013Petty":[51],"problem":[52],"for":[53,61],"arbitrary":[54],"measures":[55,62],"corresponding":[58],"hyperplane":[59],"inequality":[60],"bodies.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}