{"id":"https://openalex.org/W7220724666","doi":"https://doi.org/10.48550/arxiv.2610.03968","title":"Orientability of metric manifolds and metric spaces with curvature bounds","display_name":"Orientability of metric manifolds and metric spaces with curvature bounds","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220724666","doi":"https://doi.org/10.48550/arxiv.2610.03968"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03968","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03968","pdf_url":"https://arxiv.org/pdf/2610.03968","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/2610.03968","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054449742","display_name":"Nicola Cavallucci","orcid":"https://orcid.org/0000-0002-2785-1951","observed_orcids":["https://orcid.org/0000-0002-2785-1951"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cavallucci, Nicola","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083579939","display_name":"Denis Marti","orcid":"https://orcid.org/0009-0000-9745-6220","observed_orcids":["https://orcid.org/0009-0000-9745-6220"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marti, Denis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015153981","display_name":"Andrea Mondino","orcid":"https://orcid.org/0000-0002-1932-7148","observed_orcids":["https://orcid.org/0000-0002-1932-7148"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mondino, Andrea","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5027542189","display_name":"Raquel Perales","orcid":"https://orcid.org/0000-0002-7618-0197","observed_orcids":["https://orcid.org/0000-0002-7618-0197"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Perales, Raquel","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":0.9984999895095825,"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":0.0005000000237487257,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.00039999998989515007,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/orientability","display_name":"orientability","score":0.9850000143051147},{"id":"https://openalex.org/keywords/rectifiable-currents","display_name":"rectifiable currents","score":0.9279999732971191},{"id":"https://openalex.org/keywords/rcd-spaces","display_name":"RCD spaces","score":0.7450000047683716},{"id":"https://openalex.org/keywords/stokes-theorem","display_name":"Stokes' theorem","score":0.6610000133514404},{"id":"https://openalex.org/keywords/topological-degree","display_name":"topological degree","score":0.6399999856948853},{"id":"https://openalex.org/keywords/hausdorff-measure","display_name":"Hausdorff measure","score":0.7990000247955322},{"id":"https://openalex.org/keywords/poincare-inequality","display_name":"Poincar\u00e9 inequality","score":0.8539999723434448},{"id":"https://openalex.org/keywords/branching","display_name":"branching","score":0.4169999957084656},{"id":"https://openalex.org/keywords/homology-manifolds","display_name":"homology manifolds","score":0.7829999923706055},{"id":"https://openalex.org/keywords/curvature-bounds","display_name":"curvature bounds","score":0.6710000038146973}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8666999936103821},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5673999786376953},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5570999979972839},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4560000002384186},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C73225184","wikidata":"https://www.wikidata.org/wiki/Q1591095","display_name":"Hausdorff measure","level":3,"score":0.4154999852180481},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.41019999980926514},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4032999873161316},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3889999985694885},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.37459999322891235},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.32829999923706055},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.3264999985694885},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.3208000063896179},{"id":"https://openalex.org/C183517385","wikidata":"https://www.wikidata.org/wiki/Q855112","display_name":"Riemann curvature tensor","level":3,"score":0.3118000030517578},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2904999852180481},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03968","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03968","pdf_url":"https://arxiv.org/pdf/2610.03968","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.2610.03968","doi":"https://doi.org/10.48550/arxiv.2610.03968","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03968","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:2610.03968","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03968","pdf_url":"https://arxiv.org/pdf/2610.03968","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/G5564277497","display_name":"H\u00f6lder mappings, isoperimetric fillings, and uniformization in metric spaces","funder_award_id":"212867","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220724666.pdf","grobid_xml":"https://content.openalex.org/works/W7220724666.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W4362732802","https://openalex.org/W4382323205","https://openalex.org/W4405715454","https://openalex.org/W4405902467","https://openalex.org/W4406123271","https://openalex.org/W4406317805","https://openalex.org/W7127189379","https://openalex.org/W7127622535","https://openalex.org/W7131896888","https://openalex.org/W7140605440","https://openalex.org/W7165776562","https://openalex.org/W7204227570"],"related_works":["https://openalex.org/W2962847743","https://openalex.org/W4405902467","https://openalex.org/W7127622535","https://openalex.org/W3167629302","https://openalex.org/W7131896888","https://openalex.org/W4411131863","https://openalex.org/W2540564792","https://openalex.org/W7008912874","https://openalex.org/W2972561930","https://openalex.org/W7131071331"],"abstract_inverted_index":{"We":[0,51],"develop":[1],"a":[2,56,89,149],"theory":[3],"of":[4,44,58,67,80,95,104,142,173],"orientability":[5],"for":[6],"metric":[7,11],"manifolds":[8,159],"and":[9,29,66,70,73,147,160,167],"singular":[10,59,174],"spaces":[12,60,131],"using":[13],"locally":[14,21,40,128],"integral":[15],"currents.":[16],"For":[17,82,125],"topological":[18,34],"$n$-manifolds":[19],"with":[20,108,132],"finite":[22],"Hausdorff":[23,120],"measure,":[24,69],"we":[25,87,137],"introduce":[26],"local":[27,78,133,140,150],"degree":[28],"measure-theoretic":[30],"conditions":[31],"under":[32,77],"which":[33],"orientations":[35],"correspond":[36],"canonically":[37],"to":[38,55,170],"boundaryless,":[39],"integer":[41],"rectifiable":[42,49],"$n$-currents":[43],"multiplicity":[45,109],"one":[46],"on":[47,122],"the":[48,93,96,100,105,118,162],"part.":[50],"extend":[52],"these":[53],"currents":[54],"class":[57,172],"whose":[61],"manifold":[62],"part":[63],"is":[64,99,116],"dense":[65],"full":[68],"establish":[71],"constancy":[72],"top-dimensional":[74],"homology":[75,158],"results":[76],"uniqueness":[79,141],"orientation.":[81],"orientable":[83],"non-collapsed":[84],"$\\RCD(\u03ba,n)$":[85],"spaces,":[86],"prove":[88],"current-theoretic":[90],"Stokes":[91],"theorem:":[92],"boundary":[94],"orientation":[97,102,143],"current":[98,103],"induced":[101],"geometric":[106],"boundary,":[107],"one.":[110],"In":[111],"particular,":[112],"its":[113],"mass":[114],"measure":[115,121],"precisely":[117],"$(n-1)$-dimensional":[119],"that":[123,139],"boundary.":[124],"purely":[126],"$n$-dimensional,":[127],"geodesically":[129],"complete":[130],"upper":[134],"curvature":[135],"bounds,":[136],"show":[138],"excludes":[144],"codimension-one":[145],"branching":[146],"implies":[148],"$1$-Poincar\u00e9":[151],"inequality.":[152],"The":[153],"latter":[154],"result":[155],"applies":[156],"beyond":[157],"extends":[161],"connection":[163],"between":[164],"quantitative":[165],"topology":[166],"Poincar\u00e9":[168],"inequalities":[169],"this":[171],"spaces.":[175]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}