{"id":"https://openalex.org/W7203489318","doi":"https://doi.org/10.48550/arxiv.2608.13124","title":"Limits of mapping packages and tangents of Sobolev maps","display_name":"Limits of mapping packages and tangents of Sobolev maps","publication_year":2026,"publication_date":"2026-08-13","ids":{"openalex":"https://openalex.org/W7203489318","doi":"https://doi.org/10.48550/arxiv.2608.13124"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.13124","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13124","pdf_url":"https://arxiv.org/pdf/2608.13124","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/2608.13124","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5145617815","display_name":"Milica Cakovi\u0107","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cakovi\u0107, Milica","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5024411845","display_name":"Elefterios Soultanis","orcid":"https://orcid.org/0000-0001-9514-3941","observed_orcids":["https://orcid.org/0000-0001-9514-3941"]},"institutions":[{"id":"https://openalex.org/I94722563","display_name":"University of Jyv\u00e4skyl\u00e4","ror":"https://ror.org/05n3dz165","country_code":"FI","type":"education","lineage":["https://openalex.org/I94722563"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Soultanis, Elefterios","raw_affiliation_strings":["Department of Mathematics and Statistics , P.O. Box 35 , FI-40014 University of Jyvaskyla ;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , P.O. Box 35 , FI-40014 University of Jyvaskyla ;","institution_ids":["https://openalex.org/I94722563"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9984999895095825,"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":0.9984999895095825,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.00019999999494757503,"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":0.00019999999494757503,"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/arzela-ascoli-theorem","display_name":"Arzel\u00e0-Ascoli theorem","score":0.8640000224113464}],"concepts":[{"id":"https://openalex.org/C50335755","wikidata":"https://www.wikidata.org/wiki/Q483247","display_name":"Phenomenon","level":2,"score":0.7498999834060669},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6732000112533569},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6306999921798706},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5733000040054321},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4595000147819519},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.4465999901294708},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.43799999356269836},{"id":"https://openalex.org/C53936288","wikidata":"https://www.wikidata.org/wiki/Q2634828","display_name":"Inverse limit","level":2,"score":0.4235000014305115},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.414000004529953},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37209999561309814},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3296000063419342},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2540999948978424}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.13124","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13124","pdf_url":"https://arxiv.org/pdf/2608.13124","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.2608.13124","doi":"https://doi.org/10.48550/arxiv.2608.13124","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.13124","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:2608.13124","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13124","pdf_url":"https://arxiv.org/pdf/2608.13124","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/F4320320847","display_name":"Science Foundation Ireland","ror":"https://ror.org/0271asj38"},{"id":"https://openalex.org/F4320322733","display_name":"Ministerstwo Edukacji i Nauki","ror":"https://ror.org/05dwvd537"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203489318.pdf","grobid_xml":"https://content.openalex.org/works/W7203489318.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7134035871","https://openalex.org/W4416136105","https://openalex.org/W2056787060","https://openalex.org/W4410575400","https://openalex.org/W3129359075","https://openalex.org/W7163552615","https://openalex.org/W2602550259","https://openalex.org/W2075133657","https://openalex.org/W7220650476","https://openalex.org/W3014833090"],"abstract_inverted_index":{"We":[0,39],"show":[1],"the":[2,21,43,47,58],"existence":[3],"of":[4,6,8,60,69,95],"ultralimits":[5],"sequences":[7],"Hajlasz-Sobolev":[9,73],"mappings":[10,44],"$f_i:X_i\\to":[11],"Y_i$":[12],"when":[13],"$X_i$":[14],"converges":[15],"to":[16,46,84],"a":[17,50,67,128],"limit":[18],"space":[19],"in":[20,31,49,57],"pointed":[22,123],"measured":[23,124],"Gromov":[24],"(pmG)":[25],"sense,":[26,52],"partially":[27],"extending":[28,82],"recent":[29],"results":[30],"[T.":[32],"Ikonen":[33],"and":[34,53,110],"S.":[35],"Wenger,":[36],"(2026),":[37],"arXiv:2603.05246].":[38],"moreover":[40],"demonstrate":[41],"that":[42],"pmG-converge":[45],"ultralimit":[48],"suitable":[51],"obtain":[54],"Arzela-Ascoli":[55],"theorems":[56],"context":[59],"pmG-convergence.":[61],"As":[62],"an":[63],"application,":[64],"we":[65],"establish":[66],"version":[68],"Preiss's":[70,96],"phenomenon":[71,97],"for":[72,122],"maps":[74,85],"$f:(X,\u03bc)\\to":[75],"V$":[76],"into":[77,86],"arbitrary":[78],"Banach":[79],"spaces.":[80],"Besides":[81],"it":[83,121],"infinite":[87],"dimensional":[88],"targets,":[89],"our":[90],"result":[91],"generalizes":[92],"existing":[93],"versions":[94],"[G.":[98],"C.":[99],"David,":[100],"Geom.":[101],"Funct.":[102],"Anal.,":[103],"25":[104],"(2015)],":[105],"[N.":[106],"Gigli,":[107],"A.":[108],"Mondino,":[109],"T.":[111],"Rajala,":[112],"J.":[113],"Reine":[114],"Angew.":[115],"Math.,":[116],"705":[117],"(2015)]":[118],"by":[119],"establishing":[120],"Gromov-Hausdorff":[125],"tangents":[126],"without":[127],"doubling":[129],"assumption.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-15T00:00:00"}