{"id":"https://openalex.org/W2986262306","doi":"https://doi.org/10.1007/s00454-019-00148-0","title":"A New Approach to the Minkowski First Mixed Volume and the LYZ Conjecture","display_name":"A New Approach to the Minkowski First Mixed Volume and the LYZ Conjecture","publication_year":2019,"publication_date":"2019-11-14","ids":{"openalex":"https://openalex.org/W2986262306","doi":"https://doi.org/10.1007/s00454-019-00148-0","mag":"2986262306"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-019-00148-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-019-00148-0","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"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/A5065311964","display_name":"Xinbao Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xinbao Lu","raw_affiliation_strings":["School of Mathematical Sciences, Tongji University, Shanghai, 200092, People\u2019s Republic of China","School of Mathematical Sciences, Tongji University, Shanghai, 200092, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tongji University, Shanghai, 200092, People\u2019s Republic of China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"School of Mathematical Sciences, Tongji University, Shanghai, 200092, People's Republic of China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101888378","display_name":"Qiang Sun","orcid":"https://orcid.org/0000-0003-2479-1137"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiang Sun","raw_affiliation_strings":["School of Mathematical Sciences, Tongji University, Shanghai, 200092, People\u2019s Republic of China","School of Mathematical Sciences, Tongji University, Shanghai, 200092, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tongji University, Shanghai, 200092, People\u2019s Republic of China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"School of Mathematical Sciences, Tongji University, Shanghai, 200092, People's Republic of China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114150267","display_name":"Ge Xiong","orcid":null},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ge Xiong","raw_affiliation_strings":["School of Mathematical Sciences, Tongji University, Shanghai, 200092, People\u2019s Republic of China","School of Mathematical Sciences, Tongji University, Shanghai, 200092, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tongji University, Shanghai, 200092, People\u2019s Republic of China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"School of Mathematical Sciences, Tongji University, Shanghai, 200092, People's Republic of China","institution_ids":["https://openalex.org/I116953780"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065311964"],"corresponding_institution_ids":["https://openalex.org/I116953780"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.6646,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.67455254,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"66","issue":"1","first_page":"122","last_page":"139"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9998999834060669,"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":0.9998999834060669,"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/T13335","display_name":"Pharmacological Effects of Medicinal Plants","score":0.9186000227928162,"subfield":{"id":"https://openalex.org/subfields/2736","display_name":"Pharmacology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mixed-volume","display_name":"Mixed volume","score":0.8315754532814026},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.818703293800354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.802432656288147},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.7784050703048706},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7494872808456421},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6065236926078796},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6024186611175537},{"id":"https://openalex.org/keywords/minkowski-addition","display_name":"Minkowski addition","score":0.5426415205001831},{"id":"https://openalex.org/keywords/minkowski-inequality","display_name":"Minkowski inequality","score":0.5158256888389587},{"id":"https://openalex.org/keywords/zh\u00e0ng","display_name":"Zh\u00e0ng","score":0.4507642686367035},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4398331046104431},{"id":"https://openalex.org/keywords/convex-geometry","display_name":"Convex geometry","score":0.4284893572330475},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4215811491012573},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.3809548318386078},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28648459911346436},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.2527981400489807},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2200092375278473},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.19750988483428955},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1846272051334381},{"id":"https://openalex.org/keywords/rearrangement-inequality","display_name":"Rearrangement inequality","score":0.09452134370803833},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.059884071350097656}],"concepts":[{"id":"https://openalex.org/C44550424","wikidata":"https://www.wikidata.org/wiki/Q4424496","display_name":"Mixed volume","level":5,"score":0.8315754532814026},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.818703293800354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.802432656288147},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.7784050703048706},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7494872808456421},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6065236926078796},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6024186611175537},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.5426415205001831},{"id":"https://openalex.org/C102379996","wikidata":"https://www.wikidata.org/wiki/Q755092","display_name":"Minkowski inequality","level":5,"score":0.5158256888389587},{"id":"https://openalex.org/C2777045944","wikidata":"https://www.wikidata.org/wiki/Q12170198","display_name":"Zh\u00e0ng","level":3,"score":0.4507642686367035},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4398331046104431},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.4284893572330475},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4215811491012573},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.3809548318386078},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28648459911346436},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.2527981400489807},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2200092375278473},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.19750988483428955},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1846272051334381},{"id":"https://openalex.org/C126087398","wikidata":"https://www.wikidata.org/wiki/Q1149189","display_name":"Rearrangement inequality","level":4,"score":0.09452134370803833},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.059884071350097656},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C191935318","wikidata":"https://www.wikidata.org/wiki/Q148","display_name":"China","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-019-00148-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-019-00148-0","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6000000238418579}],"awards":[{"id":"https://openalex.org/G335464223","display_name":null,"funder_award_id":"11871373","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W158064062","https://openalex.org/W1549716940","https://openalex.org/W1595077564","https://openalex.org/W1606263708","https://openalex.org/W1832993423","https://openalex.org/W1963777701","https://openalex.org/W1984361581","https://openalex.org/W2000270585","https://openalex.org/W2025475361","https://openalex.org/W2026918434","https://openalex.org/W2036591532","https://openalex.org/W2064022833","https://openalex.org/W2079679648","https://openalex.org/W2080387137","https://openalex.org/W2087425625","https://openalex.org/W2149194571","https://openalex.org/W2333141878","https://openalex.org/W2937222619","https://openalex.org/W2946516028","https://openalex.org/W2964109132"],"related_works":["https://openalex.org/W4298216311","https://openalex.org/W2952223369","https://openalex.org/W3102349276","https://openalex.org/W4286418619","https://openalex.org/W36492929","https://openalex.org/W4388767834","https://openalex.org/W2360902574","https://openalex.org/W3196950278","https://openalex.org/W2271848893","https://openalex.org/W4386099291"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
