{"id":"https://openalex.org/W4417517419","doi":"https://doi.org/10.1090/tran/9866","title":"The capillary \ud835\udc3f_{\ud835\udc5d}-Minkowski problem","display_name":"The capillary \ud835\udc3f_{\ud835\udc5d}-Minkowski problem","publication_year":2026,"publication_date":"2026-06-24","ids":{"openalex":"https://openalex.org/W4417517419","doi":"https://doi.org/10.1090/tran/9866"},"language":"en","primary_location":{"id":"doi:10.1090/tran/9866","doi":"https://doi.org/10.1090/tran/9866","is_oa":false,"landing_page_url":"https://doi.org/10.1090/tran/9866","pdf_url":null,"source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2505.07746","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035002584","display_name":"Xinqun Mei","orcid":"https://orcid.org/0000-0003-2092-7834","observed_orcids":["https://orcid.org/0000-0003-2092-7834"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xinqun Mei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054085447","display_name":"Guofang Wang","orcid":"https://orcid.org/0000-0003-2727-2607","observed_orcids":["https://orcid.org/0000-0003-2727-2607"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guofang Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000930886","display_name":"Liangjun Weng","orcid":"https://orcid.org/0000-0002-5304-3325","observed_orcids":["https://orcid.org/0000-0002-5304-3325"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liangjun Weng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":24.1794,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.99791755,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.8798999786376953,"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":0.8798999786376953,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.10329999774694443,"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":0.0024999999441206455,"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/lp-minkowski-problem","display_name":"Lp Minkowski problem","score":0.8429999947547913},{"id":"https://openalex.org/keywords/robin-boundary-conditions","display_name":"Robin boundary conditions","score":0.9300000071525574},{"id":"https://openalex.org/keywords/monge-ampere-equation","display_name":"Monge-Amp\u00e8re equation","score":0.9769999980926514},{"id":"https://openalex.org/keywords/spherical-caps","display_name":"spherical caps","score":0.5830000042915344}],"concepts":[{"id":"https://openalex.org/C196806460","wikidata":"https://www.wikidata.org/wiki/Q188603","display_name":"Capillary action","level":2,"score":0.8206999897956848},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.5985999703407288},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5504999756813049},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5439000129699707},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.49799999594688416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.486299991607666},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.45249998569488525},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.4339999854564667},{"id":"https://openalex.org/C72550971","wikidata":"https://www.wikidata.org/wiki/Q5035397","display_name":"Capillary surface","level":3,"score":0.4332999885082245},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4101000130176544},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3634999990463257},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.36309999227523804},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29739999771118164},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2903999984264374},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.2833000123500824},{"id":"https://openalex.org/C48797263","wikidata":"https://www.wikidata.org/wiki/Q4212891","display_name":"Capillary pressure","level":4,"score":0.27300000190734863},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.2630999982357025}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/tran/9866","doi":"https://doi.org/10.1090/tran/9866","is_oa":false,"landing_page_url":"https://doi.org/10.1090/tran/9866","pdf_url":null,"source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2505.07746","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2505.07746","pdf_url":"https://arxiv.org/pdf/2505.07746","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":"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2505.07746","doi":"https://doi.org/10.48550/arxiv.2505.07746","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.07746","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:2505.07746","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2505.07746","pdf_url":"https://arxiv.org/pdf/2505.07746","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":"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G28096953","display_name":null,"funder_award_id":"2020YFA0712800","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G3261117727","display_name":null,"funder_award_id":"2025M773082","funder_id":"https://openalex.org/F4320333371","funder_display_name":"Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore"},{"id":"https://openalex.org/G4289148511","display_name":null,"funder_award_id":"2025M773082","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4535941165","display_name":null,"funder_award_id":"2025M773082","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5548414551","display_name":null,"funder_award_id":"2025T180843","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G5666124546","display_name":null,"funder_award_id":"2020YFA0712800","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5944313541","display_name":null,"funder_award_id":"2025T180843","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G6989957557","display_name":null,"funder_award_id":"2020YFA0712800","funder_id":"https://openalex.org/F4320333371","funder_display_name":"Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore"},{"id":"https://openalex.org/G8398680159","display_name":null,"funder_award_id":"2025T180843","funder_id":"https://openalex.org/F4320333371","funder_display_name":"Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore"}],"funders":[{"id":"https://openalex.org/F4320311012","display_name":"Scuola Normale Superiore","ror":"https://ror.org/03aydme10"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320324499","display_name":"Universit\u00e0 di Pisa","ror":"https://ror.org/03ad39j10"},{"id":"https://openalex.org/F4320333371","display_name":"Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore","ror":"https://ror.org/04rcbrx45"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4417517419.pdf","grobid_xml":"https://content.openalex.org/works/W4417517419.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4391988240","https://openalex.org/W4416191039","https://openalex.org/W6910869458"],"related_works":["https://openalex.org/W4415273628","https://openalex.org/W7212051130","https://openalex.org/W7116061381","https://openalex.org/W4415087258","https://openalex.org/W7133355749","https://openalex.org/W7214961566","https://openalex.org/W7215133679","https://openalex.org/W4408961109","https://openalex.org/W4417530927","https://openalex.org/W4417302333"],"abstract_inverted_index":{"This":[0,52],"paper":[1],"is":[2],"a":[3,26,37,42,55,92,96],"continuation":[4],"of":[5,60],"our":[6],"recent":[7],"work":[8],"[Adv.":[9],"Math.":[10],"469":[11],"(2025),":[12],"Paper":[13],"No.":[14],"110230]":[15],"concerning":[16],"the":[17,49,61,80,85,101],"capillary":[18,27,38,44,81],"Minkowski":[19],"problem.":[20],"We":[21],"propose,":[22],"in":[23,48,84],"this":[24],"paper,":[25],"$L_p$-Minkowski":[28,63,82],"problem":[29,64,83],"for":[30],"$p\\in":[31],"\\mathbb{R}$,":[32],"which":[33],"seeks":[34],"to":[35,91],"find":[36],"convex":[39],"body":[40],"with":[41,95],"prescribed":[43],"$L_p$-surface":[45],"area":[46],"measure":[47],"Euclidean":[50],"half-space.":[51],"formulation":[53],"provides":[54],"natural":[56],"Robin":[57,97],"boundary":[58,98],"analogue":[59],"classical":[62],"introduced":[65],"by":[66,88],"Lutwak":[67],"[J.":[68],"Differential":[69],"Geom.":[70],"38":[71],"(1993),":[72],"no.":[73],"1,":[74],"131--150].":[75],"For":[76],"$p>1$,":[77],"we":[78],"resolve":[79],"smooth":[86],"category":[87],"reducing":[89],"it":[90],"Monge--Amp\u00e8re":[93],"equation":[94],"condition":[99],"on":[100],"unit":[102],"spherical":[103],"cap.":[104]},"counts_by_year":[{"year":2026,"cited_by_count":11},{"year":2025,"cited_by_count":5}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2025-10-10T00:00:00"}