{"id":"https://openalex.org/W7220970406","doi":"https://doi.org/10.48550/arxiv.2610.10337","title":"The stability of Sharp Poincar\u00e9 and Brascamp--Lieb inequalities with full monomial weights","display_name":"The stability of Sharp Poincar\u00e9 and Brascamp--Lieb inequalities with full monomial weights","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220970406","doi":"https://doi.org/10.48550/arxiv.2610.10337"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10337","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10337","pdf_url":"https://arxiv.org/pdf/2610.10337","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.10337","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043235505","display_name":"Nguyen Lam","orcid":"https://orcid.org/0000-0002-8392-6284","observed_orcids":["https://orcid.org/0000-0002-8392-6284"]},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lam, Nguyen","raw_affiliation_strings":["Department of Mathematics , University of Connecticut , Storrs , CT 06269 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Connecticut , Storrs , CT 06269 , USA","institution_ids":["https://openalex.org/I140172145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157972017","display_name":"Guozhen Lu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lu, Guozhen","raw_affiliation_strings":["Department of Mathematics , University of Connecticut , Storrs , CT 06269 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Connecticut , Storrs , CT 06269 , USA","institution_ids":["https://openalex.org/I140172145"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5122392273","display_name":"Andrey Russanov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Russanov, Andrey","raw_affiliation_strings":["Department of Mathematics , University of Connecticut , Storrs , CT 06269 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Connecticut , Storrs , CT 06269 , USA","institution_ids":["https://openalex.org/I140172145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I140172145"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9785000085830688,"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":0.9785000085830688,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.01769999973475933,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.0008999999845400453,"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/brascamp-lieb-inequality","display_name":"Brascamp-Lieb inequality","score":0.9879999756813049},{"id":"https://openalex.org/keywords/gaussian-measure","display_name":"Gaussian measure","score":0.8709999918937683},{"id":"https://openalex.org/keywords/curvature-dimension-condition","display_name":"curvature-dimension condition","score":0.8489999771118164},{"id":"https://openalex.org/keywords/logarithmic-sobolev-inequality","display_name":"logarithmic Sobolev inequality","score":0.9409999847412109},{"id":"https://openalex.org/keywords/hypercontractivity","display_name":"hypercontractivity","score":0.9020000100135803},{"id":"https://openalex.org/keywords/gradient-stability","display_name":"gradient stability","score":0.777999997138977},{"id":"https://openalex.org/keywords/ornstein-uhlenbeck-operator","display_name":"Ornstein-Uhlenbeck operator","score":0.9039999842643738},{"id":"https://openalex.org/keywords/convex-cones","display_name":"convex cones","score":0.8130000233650208}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8840000033378601},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.7337999939918518},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.58160001039505},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5467000007629395},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4699000120162964},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.445499986410141},{"id":"https://openalex.org/C185644265","wikidata":"https://www.wikidata.org/wiki/Q3711848","display_name":"Sobolev inequality","level":3,"score":0.40540000796318054},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3917999863624573},{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.3889000117778778},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38830000162124634},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.37959998846054077},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3425999879837036},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.3321000039577484},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3240000009536743},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.3167000114917755},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.29789999127388},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C2777789435","wikidata":"https://www.wikidata.org/wiki/Q19369206","display_name":"Monomial ideal","level":4,"score":0.2842000126838684},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2712000012397766},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.2639000117778778}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10337","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10337","pdf_url":"https://arxiv.org/pdf/2610.10337","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.2610.10337","doi":"https://doi.org/10.48550/arxiv.2610.10337","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10337","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.10337","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10337","pdf_url":"https://arxiv.org/pdf/2610.10337","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220970406.pdf","grobid_xml":"https://content.openalex.org/works/W7220970406.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W4387596003","https://openalex.org/W4406231704","https://openalex.org/W4416948273","https://openalex.org/W7131320089","https://openalex.org/W7155086238","https://openalex.org/W7164040762","https://openalex.org/W7203700328","https://openalex.org/W7213956424","https://openalex.org/W7214039301","https://openalex.org/W7220848326"],"related_works":["https://openalex.org/W7119499983","https://openalex.org/W6929335424","https://openalex.org/W7155086238","https://openalex.org/W7164040762","https://openalex.org/W7123297306","https://openalex.org/W3165877102","https://openalex.org/W3104799488","https://openalex.org/W4319298853","https://openalex.org/W2883320289","https://openalex.org/W7128686689"],"abstract_inverted_index":{"It":[0],"was":[1],"known":[2],"that":[3,112],"the":[4,11,25,30,44,52,65,74,77,99,104,114,122,131,142,151,168,207,211,215],"Gaussian":[5,45,83,93],"measures":[6,46,94],"with":[7,34,47,69,154,171],"monomial":[8,36,49,82,156,176],"weights":[9,50,187],"satisfy":[10,51],"sharp":[12,26,66,100,115,147,208],"pointwise":[13],"curvature-dimension":[14,54,198],"condition":[15,55,204],"$CD(1,":[16],"\\infty)$,":[17],"and":[18,73,103,117,145,162,205],"consequently":[19],"they":[20],"allow":[21],"us":[22,62],"to":[23,63,91,184],"derive":[24,137],"constant":[27,71,209],"$1$":[28],"for":[29,61,80,141,150,167,210],"Poincar\u00e9":[31,67,101,116,143,152,212],"inequality":[32,79,102,111,153,170,213],"only":[33],"partial":[35],"weights.":[37,157],"In":[38],"this":[39],"paper,":[40],"we":[41,106,136,193],"first":[42],"establish":[43,160],"full":[48,81,155],"integrated":[53,197],"$ICD(2,":[56],"\\infty)$":[57],"which":[58],"is":[59],"sufficient":[60],"prove":[64],"inequalities":[68],"optimal":[70],"$2$":[72],"stability":[75,149,165],"of":[76,86,130],"Brascamp--Lieb":[78,169],"measures.":[84],"Several":[85],"these":[87],"results":[88],"are":[89],"extended":[90],"homogeneous":[92,186],"on":[95],"convex":[96],"cones.":[97],"Using":[98],"hypercontractivity,":[105],"obtain":[107,146,194],"an":[108,138,195],"improved":[109,196],"Beckner":[110],"recover":[113],"logarithmic":[118],"Sobolev":[119],"constants":[120,173],"at":[121],"endpoints.":[123],"By":[124],"developing":[125],"a":[126,189,201],"Laguerre":[127],"spectral":[128],"decomposition":[129],"associated":[132],"Ornstein--Uhlenbeck":[133],"type":[134],"generator,":[135],"exact":[139],"identity":[140],"deficit":[144],"gradient":[148,164],"We":[158],"further":[159],"$L^2$":[161,181],"weighted":[163],"estimates":[166],"explicit":[172],"when":[174],"all":[175],"exponents":[177],"exceed":[178],"$1$.":[179],"The":[180],"estimate":[182],"extends":[183],"log-concave":[185],"under":[188,200],"subharmonicity":[190],"assumption.":[191],"Finally,":[192],"bound":[199],"scale-invariant":[202],"Hessian":[203],"identify":[206],"in":[214],"radial":[216],"class.":[217]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}