{"id":"https://openalex.org/W7214795462","doi":"https://doi.org/10.48550/arxiv.2609.34751","title":"The Asymptotic Plateau Problem for $p$-Convex Hypersurfaces in Hyperbolic Space","display_name":"The Asymptotic Plateau Problem for $p$-Convex Hypersurfaces in Hyperbolic Space","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214795462","doi":"https://doi.org/10.48550/arxiv.2609.34751"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.34751","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34751","pdf_url":"https://arxiv.org/pdf/2609.34751","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/2609.34751","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061535311","display_name":"Shujun Shi","orcid":"https://orcid.org/0000-0002-3880-7884","observed_orcids":["https://orcid.org/0000-0002-3880-7884"]},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shi, Shujun","raw_affiliation_strings":["Institute for Advanced Study in Mathematics of HIT , Harbin Institute of Technol- ogy , Harbin , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Advanced Study in Mathematics of HIT , Harbin Institute of Technol- ogy , Harbin , China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042968954","display_name":"Zhenan Sui","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sui, Zhenan","raw_affiliation_strings":["Institute for Advanced Study in Mathematics of HIT , Harbin Institute of Technol- ogy , Harbin , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Advanced Study in Mathematics of HIT , Harbin Institute of Technol- ogy , Harbin , China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I204983213"],"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":0.9897000193595886,"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":0.9897000193595886,"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":0.006800000090152025,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.0015999999595806003,"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/hyperbolic-space","display_name":"hyperbolic space","score":0.9919999837875366},{"id":"https://openalex.org/keywords/prescribed-mean-curvature-equation","display_name":"prescribed mean curvature","score":0.9049999713897705},{"id":"https://openalex.org/keywords/principal-curvatures","display_name":"principal curvatures","score":0.7260000109672546},{"id":"https://openalex.org/keywords/curvature-estimates","display_name":"curvature estimates","score":0.7009999752044678},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.8270000219345093}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8734999895095825},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.6608999967575073},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6535000205039978},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.60589998960495},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6033999919891357},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6014999747276306},{"id":"https://openalex.org/C16977076","wikidata":"https://www.wikidata.org/wiki/Q1589551","display_name":"Principal curvature","level":4,"score":0.5849999785423279},{"id":"https://openalex.org/C83677898","wikidata":"https://www.wikidata.org/wiki/Q1878538","display_name":"Hyperbolic space","level":2,"score":0.5824000239372253},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5271999835968018},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4555000066757202},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.44940000772476196},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4458000063896179},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.3752000033855438},{"id":"https://openalex.org/C82673646","wikidata":"https://www.wikidata.org/wiki/Q2246553","display_name":"Hyperbolic triangle","level":4,"score":0.36739999055862427},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.3580000102519989},{"id":"https://openalex.org/C2780030769","wikidata":"https://www.wikidata.org/wiki/Q4968575","display_name":"Plateau (mathematics)","level":2,"score":0.3522999882698059},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.3319000005722046},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.2930000126361847},{"id":"https://openalex.org/C91588493","wikidata":"https://www.wikidata.org/wiki/Q644719","display_name":"Half-space","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26660001277923584},{"id":"https://openalex.org/C2778433361","wikidata":"https://www.wikidata.org/wiki/Q7268358","display_name":"Quadratic differential","level":3,"score":0.26159998774528503},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2614000141620636},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C152022596","wikidata":"https://www.wikidata.org/wiki/Q7268361","display_name":"Quadratic form (statistics)","level":2,"score":0.2556000053882599},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.2542000114917755},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.34751","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34751","pdf_url":"https://arxiv.org/pdf/2609.34751","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.2609.34751","doi":"https://doi.org/10.48550/arxiv.2609.34751","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.34751","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:2609.34751","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34751","pdf_url":"https://arxiv.org/pdf/2609.34751","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":[{"id":"https://openalex.org/G5665659986","display_name":null,"funder_award_id":"PL2025A006","funder_id":"https://openalex.org/F4320323085","funder_display_name":"Natural Science Foundation of Heilongjiang Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323085","display_name":"Natural Science Foundation of Heilongjiang Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214795462.pdf","grobid_xml":"https://content.openalex.org/works/W7214795462.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4414768987","https://openalex.org/W4414891034","https://openalex.org/W7154610388","https://openalex.org/W7206163258","https://openalex.org/W7206163746"],"related_works":["https://openalex.org/W4318775791","https://openalex.org/W4285203257","https://openalex.org/W4413399088","https://openalex.org/W1567965987","https://openalex.org/W7172485202","https://openalex.org/W7206163258","https://openalex.org/W4417159293","https://openalex.org/W1655635840","https://openalex.org/W4402533228","https://openalex.org/W3153434130"],"abstract_inverted_index":{"We":[0],"solve":[1],"the":[2,10,14,19,23,60,67,79,84,95,101,117],"asymptotic":[3,54],"Plateau":[4],"problem":[5],"in":[6,83,122],"hyperbolic":[7],"space":[8],"for":[9,94],"curvature":[11,51,72,120],"given":[12],"by":[13],"normalized":[15],"geometric":[16],"mean":[17],"of":[18,22],"$p$-fold":[20],"sums":[21],"principal":[24,119],"curvatures.":[25],"For":[26],"every":[27],"$n\\ge3$,":[28],"$2\\le":[29],"p\\le":[30],"n-1$,":[31],"and":[32,53,64,111],"$\u03c3\\in(0,1)$,":[33],"each":[34],"bounded":[35],"domain":[36],"$\u03a9\\subset\\mathbb{R}^n$":[37],"with":[38,49,76,108],"smooth":[39],"mean-convex":[40],"boundary":[41,55,81],"admits":[42],"a":[43,104,112,123],"unique":[44],"complete":[45],"admissible":[46],"vertical":[47],"graph":[48],"prescribed":[50],"$\u03c3$":[52],"$\\partial\u03a9\\times\\{0\\}$.":[56],"The":[57,70,88],"result":[58],"extends":[59],"known":[61],"cases":[62],"$(n,p)=(3,2)$":[63],"$(4,3)$":[65],"to":[66,78],"stated":[68],"range.":[69,125],"key":[71],"estimate":[73],"is":[74],"uniform":[75],"respect":[77],"positive":[80],"height":[82],"approximating":[85],"Dirichlet":[86],"problems.":[87],"proof":[89],"establishes":[90],"two":[91],"lower":[92],"bounds":[93],"full":[96],"third-derivative":[97],"quadratic":[98],"form":[99],"under":[100],"linearized":[102],"constraints:":[103],"sharp":[105],"universal":[106],"bound":[107,115],"coefficient":[109],"$2/p$":[110],"stronger":[113],"direction-dependent":[114],"when":[116],"relevant":[118],"lies":[121],"specified":[124]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}