{"id":"https://openalex.org/W7223109296","doi":"https://doi.org/10.48550/arxiv.2610.28572","title":"Nonlocal Equations on Domains and Manifolds Without Symmetries","display_name":"Nonlocal Equations on Domains and Manifolds Without Symmetries","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223109296","doi":"https://doi.org/10.48550/arxiv.2610.28572"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.28572","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28572","pdf_url":"https://arxiv.org/pdf/2610.28572","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/2610.28572","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159198527","display_name":"Santiago Castellanos","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Castellanos, Santiago","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159198527"],"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9937000274658203,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9937000274658203,"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":0.005400000140070915,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.00019999999494757503,"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/existence-of-solutions","display_name":"existence of solutions","score":0.7329999804496765},{"id":"https://openalex.org/keywords/regularity-of-solutions","display_name":"regularity of solutions","score":0.9729999899864197},{"id":"https://openalex.org/keywords/riemannian-manifolds","display_name":"Riemannian manifolds","score":0.7540000081062317},{"id":"https://openalex.org/keywords/cartan-hadamard-manifolds","display_name":"Cartan-Hadamard manifolds","score":0.8960000276565552},{"id":"https://openalex.org/keywords/noncompact-manifolds","display_name":"non-compact manifolds","score":0.7770000100135803},{"id":"https://openalex.org/keywords/bounded-domains","display_name":"bounded domains","score":0.703000009059906},{"id":"https://openalex.org/keywords/perturbed-equations","display_name":"perturbed equations","score":0.7680000066757202},{"id":"https://openalex.org/keywords/curvature-conditions","display_name":"curvature conditions","score":0.7269999980926514},{"id":"https://openalex.org/keywords/nonlocal-operators","display_name":"nonlocal operators","score":0.4090000092983246}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6906999945640564},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6593999862670898},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.531000018119812},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.517300009727478},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4708999991416931},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4578000009059906},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.4564000070095062},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.45500001311302185},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.43939998745918274},{"id":"https://openalex.org/C154968394","wikidata":"https://www.wikidata.org/wiki/Q5535474","display_name":"Geometric analysis","level":5,"score":0.4251999855041504},{"id":"https://openalex.org/C203934109","wikidata":"https://www.wikidata.org/wiki/Q7322952","display_name":"Ricci-flat manifold","level":4,"score":0.40130001306533813},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.3968999981880188},{"id":"https://openalex.org/C191174866","wikidata":"https://www.wikidata.org/wiki/Q17017346","display_name":"Global analysis","level":5,"score":0.3716000020503998},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.35120001435279846},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.33239999413490295},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.3221000134944916},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.30230000615119934},{"id":"https://openalex.org/C146674193","wikidata":"https://www.wikidata.org/wiki/Q40139","display_name":"Curvature of Riemannian manifolds","level":5,"score":0.30090001225471497},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.2660999894142151},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.26179999113082886}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.28572","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28572","pdf_url":"https://arxiv.org/pdf/2610.28572","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.2610.28572","doi":"https://doi.org/10.48550/arxiv.2610.28572","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.28572","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:2610.28572","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28572","pdf_url":"https://arxiv.org/pdf/2610.28572","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/G1933454274","display_name":"DIFFERENTIAL GEOMETRIC AND TOPOLOGICAL ASPECTS OF DIFFERENTIAL EQUATIONS GLOBAL ANALYSIS AND  INTEGRABLE SYSTEMS","funder_award_id":"1241719","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"}],"funders":[{"id":"https://openalex.org/F4320309589","display_name":"Universidad de Santiago de Chile","ror":"https://ror.org/02ma57s91"},{"id":"https://openalex.org/F4320331146","display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","ror":"https://ror.org/05btm5233"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223109296.pdf","grobid_xml":"https://content.openalex.org/works/W7223109296.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7223117422","https://openalex.org/W1494123753","https://openalex.org/W1994733847","https://openalex.org/W7220856512","https://openalex.org/W4224292423","https://openalex.org/W3028397359","https://openalex.org/W1734630047","https://openalex.org/W2606995605","https://openalex.org/W1611000558","https://openalex.org/W4294430769"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3],"establish":[4],"existence":[5,33],"and":[6,21,27,50],"regularity":[7],"results":[8,34],"for":[9],"solutions":[10],"to":[11],"nonlinear":[12],"nonlocal":[13],"equations":[14,45],"of":[15],"the":[16],"form":[17],"$f(\u0394)u":[18],"=":[19,23],"U(x,u)$":[20,24],"$f(\u0394_{g})u":[22],"in":[25,42],"Euclidean":[26],"Riemannian":[28,48],"settings,":[29],"respectively.":[30],"We":[31],"prove":[32],"across":[35],"three":[36],"distinct":[37],"geometric":[38,56],"scenarios:":[39],"bounded":[40],"domains":[41],"$\\mathbb{R}^n$,":[43],"perturbed":[44],"on":[46],"compact":[47],"manifolds,":[49],"noncompact":[51],"Cartan-Hadamard":[52],"manifolds":[53],"under":[54],"suitable":[55],"curvature":[57],"conditions.":[58]},"counts_by_year":[],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2026-10-22T00:00:00"}