{"id":"https://openalex.org/W7204190950","doi":"https://doi.org/10.48550/arxiv.2608.23184","title":"Semilinear overdetermined problems, a divergence formula, and geometric inequalities","display_name":"Semilinear overdetermined problems, a divergence formula, and geometric inequalities","publication_year":2026,"publication_date":"2026-08-24","ids":{"openalex":"https://openalex.org/W7204190950","doi":"https://doi.org/10.48550/arxiv.2608.23184"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.23184","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23184","pdf_url":"https://arxiv.org/pdf/2608.23184","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/2608.23184","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041227705","display_name":"Benedito Leandro","orcid":"https://orcid.org/0000-0002-8986-4141","observed_orcids":["https://orcid.org/0000-0002-8986-4141"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leandro, Benedito","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148062777","display_name":"Ilton Menezes","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Menezes, Ilton","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5027086873","display_name":"Rafael Novais","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Novais, Rafael","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":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":0.9603999853134155,"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":0.9603999853134155,"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":0.0340999998152256,"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":0.0012000000569969416,"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/neumann-boundary-conditions","display_name":"Neumann boundary conditions","score":0.8709999918937683},{"id":"https://openalex.org/keywords/asymptotically-hyperbolic-manifolds","display_name":"asymptotically hyperbolic manifolds","score":0.8790000081062317},{"id":"https://openalex.org/keywords/compact-riemannian-manifolds","display_name":"compact Riemannian manifolds","score":0.8330000042915344},{"id":"https://openalex.org/keywords/geometric-inequalities","display_name":"geometric inequalities","score":0.6460000276565552}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8420000076293945},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.614300012588501},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5698000192642212},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5547999739646912},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5210999846458435},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48579999804496765},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.482699990272522},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.44920000433921814},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4226999878883362},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.42149999737739563},{"id":"https://openalex.org/C83677898","wikidata":"https://www.wikidata.org/wiki/Q1878538","display_name":"Hyperbolic space","level":2,"score":0.4043000042438507},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.37869998812675476},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.35429999232292175},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.3458000123500824},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.32760000228881836},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.32580000162124634},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C81901731","wikidata":"https://www.wikidata.org/wiki/Q331348","display_name":"Overdetermined system","level":2,"score":0.2953999936580658},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.2922999858856201},{"id":"https://openalex.org/C119830904","wikidata":"https://www.wikidata.org/wiki/Q233220","display_name":"Second fundamental form","level":4,"score":0.2906999886035919},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.2623000144958496},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.2581000030040741}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.23184","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23184","pdf_url":"https://arxiv.org/pdf/2608.23184","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.2608.23184","doi":"https://doi.org/10.48550/arxiv.2608.23184","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.23184","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:2608.23184","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23184","pdf_url":"https://arxiv.org/pdf/2608.23184","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/G8285809817","display_name":null,"funder_award_id":"00193","funder_id":"https://openalex.org/F4320323350","funder_display_name":"Funda\u00e7\u00e3o de Apoio \u00e0 Pesquisa do Distrito Federal"}],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320323350","display_name":"Funda\u00e7\u00e3o de Apoio \u00e0 Pesquisa do Distrito Federal","ror":"https://ror.org/04djvx395"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204190950.pdf","grobid_xml":"https://content.openalex.org/works/W7204190950.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W3038588914","https://openalex.org/W4393119072"],"related_works":["https://openalex.org/W2986788534","https://openalex.org/W4415231561","https://openalex.org/W2963026207","https://openalex.org/W3162382364","https://openalex.org/W7165637306","https://openalex.org/W4302066528","https://openalex.org/W4385373932","https://openalex.org/W7131387288","https://openalex.org/W7125199207","https://openalex.org/W2756136854"],"abstract_inverted_index":{"Considering":[0],"an":[1,83,112],"$n$-dimensional":[2],"compact":[3,87],"Riemannian":[4,48],"manifold":[5],"with":[6],"a":[7,11,26,37,41,46,117],"boundary":[8,78],"that":[9,111],"satisfies":[10],"Serrin-type":[12],"problem,":[13],"we":[14,29,81,109],"prove":[15,82,110],"sharp":[16],"upper":[17],"and":[18,59,65],"lower":[19],"bounds":[20],"for":[21,40,72,86],"the":[22,31,96,104,121,127],"area":[23],"of":[24,34,95,107,116],"such":[25],"boundary.":[27],"Then,":[28],"present":[30],"main":[32,93],"result":[33,106],"this":[35,101],"paper:":[36],"divergence":[38,51,97],"formula":[39,52,98],"special":[42],"vector":[43],"field":[44],"on":[45],"given":[47],"manifold.":[49],"This":[50],"is":[53],"closely":[54],"related":[55,60],"to":[56],"sub-static":[57],"manifolds":[58,74],"metrics,":[61],"e.g.,":[62],"$V$-static,":[63],"static,":[64],"electrostatic":[66,90],"manifolds.":[67,91],"We":[68],"show":[69],"Minkowski-type":[70],"inequalities":[71],"$V$-sub-static":[73],"under":[75],"different":[76],"Neumann":[77],"conditions.":[79],"Moreover,":[80],"area-charge":[84],"inequality":[85],"(and":[88],"noncompact)":[89],"The":[92],"application":[94],"presented":[99],"in":[100],"work":[102],"generalizes":[103],"classical":[105],"Boucher--Gibbons--Horowitz:":[108],"asymptotically":[113],"hyperbolic":[114,128],"space":[115],"static":[118],"spacetime":[119],"satisfying":[120],"null":[122],"convergence":[123],"condition":[124],"must":[125],"be":[126],"space.":[129]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-26T00:00:00"}