{"id":"https://openalex.org/W7134885675","doi":"https://doi.org/10.48550/arxiv.2603.09459","title":"Nonlinear Lebesgue spaces: Curves and geometry","display_name":"Nonlinear Lebesgue spaces: Curves and geometry","publication_year":2026,"publication_date":"2026-03-10","ids":{"openalex":"https://openalex.org/W7134885675","doi":"https://doi.org/10.48550/arxiv.2603.09459"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2603.09459","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2603.09459","pdf_url":"https://arxiv.org/pdf/2603.09459","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/2603.09459","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000590225","display_name":"Guillaume Serieys","orcid":"https://orcid.org/0000-0002-1050-9703","observed_orcids":["https://orcid.org/0000-0002-1050-9703"]},"institutions":[{"id":"https://openalex.org/I4387154995","display_name":"Math\u00e9matiques Appliqu\u00e9es \u00e0 Paris 5","ror":"https://ror.org/04yrrdj53","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4387154995"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"S\u00e9rieys, Guillaume","raw_affiliation_strings":["MAP5 - UMR 8145"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MAP5 - UMR 8145","institution_ids":["https://openalex.org/I4387154995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000590225"],"corresponding_institution_ids":["https://openalex.org/I4387154995"],"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":0.9932000041007996,"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":0.9932000041007996,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.003700000001117587,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.0010999999940395355,"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/metric-spaces","display_name":"metric spaces","score":0.6570000052452087},{"id":"https://openalex.org/keywords/alexandrov-curvature","display_name":"Alexandrov curvature","score":0.8169999718666077},{"id":"https://openalex.org/keywords/length-structure","display_name":"length structure","score":0.8169999718666077}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.801800012588501},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7944999933242798},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.6686000227928162},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.612500011920929},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.6033999919891357},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5864999890327454},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5159000158309937},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.4616999924182892},{"id":"https://openalex.org/C43323394","wikidata":"https://www.wikidata.org/wiki/Q3799278","display_name":"Lebesgue\u2013Stieltjes integration","level":5,"score":0.453000009059906},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4377000033855438},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42410001158714294},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4074999988079071},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.37720000743865967},{"id":"https://openalex.org/C2777105136","wikidata":"https://www.wikidata.org/wiki/Q827230","display_name":"Lebesgue measure","level":3,"score":0.35830000042915344},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.32510000467300415},{"id":"https://openalex.org/C12871628","wikidata":"https://www.wikidata.org/wiki/Q7598372","display_name":"Standard probability space","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C10784197","wikidata":"https://www.wikidata.org/wiki/Q233858","display_name":"Non-Euclidean geometry","level":3,"score":0.31200000643730164},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.28279998898506165},{"id":"https://openalex.org/C154968394","wikidata":"https://www.wikidata.org/wiki/Q5535474","display_name":"Geometric analysis","level":5,"score":0.27239999175071716},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.26510000228881836}],"mesh":[],"locations_count":6,"locations":[{"id":"pmh:oai:arXiv.org:2603.09459","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2603.09459","pdf_url":"https://arxiv.org/pdf/2603.09459","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":"pmh:oai:HAL:hal-05544460v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05544460","pdf_url":"https://hal.science/hal-05544460/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-05544460v2","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05544460v2/document","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-05544460v3","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05544460v3/document","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-05544460v4","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05544460","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2603.09459","doi":"https://doi.org/10.48550/arxiv.2603.09459","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.09459","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:2603.09459","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2603.09459","pdf_url":"https://arxiv.org/pdf/2603.09459","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/F4320332088","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7134885675.pdf","grobid_xml":"https://content.openalex.org/works/W7134885675.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1987493708","https://openalex.org/W2147640194","https://openalex.org/W2236412176","https://openalex.org/W2724269953","https://openalex.org/W4399694283","https://openalex.org/W4406024052","https://openalex.org/W7117116384"],"related_works":["https://openalex.org/W7117116384","https://openalex.org/W2017028343","https://openalex.org/W7208467151","https://openalex.org/W7098921854","https://openalex.org/W2079164859","https://openalex.org/W7202386671","https://openalex.org/W2953084798","https://openalex.org/W1789477970","https://openalex.org/W2010798454","https://openalex.org/W2885028956"],"abstract_inverted_index":{"This":[0,110],"paper":[1],"is":[2],"the":[3,9,15,42,59,69,86,105,126,130],"second":[4],"in":[5,34,96,104],"a":[6,62,82,117],"series":[7],"by":[8],"author":[10],"and":[11,19],"collaborators":[12],"devoted":[13],"to":[14],"study":[16],"of":[17,22,30,45,61,71,85,93,107,112,129,133],"geometric":[18,47,131],"analytic":[20],"properties":[21,132],"nonlinear":[23,83,97,134],"Lebesgue":[24,98,135],"spaces,":[25],"that":[26],"is,":[27],"L^p":[28,94,108,113],"spaces":[29,99,136],"mappings":[31,101],"taking":[32,102],"values":[33,103],"arbitrary":[35],"metric":[36],"spaces.":[37],"The":[38],"present":[39],"article":[40],"formalizes":[41],"pointwise":[43,77,127],"description":[44,128],"their":[46,53],"properties---their":[48],"length":[49],"structure,":[50],"bounds":[51],"on":[52],"Alexandrov":[54],"curvature":[55],"as":[56,58],"well":[57],"definition":[60],"velocity":[63],"for":[64,120],"absolutely":[65,121],"continuous":[66,122],"curves":[67,95,114],"despite":[68],"lack":[70],"differential":[72],"structure.":[73],"To":[74],"obtain":[75],"this":[76],"description,":[78],"we":[79],"first":[80],"prove":[81],"analogue":[84],"Fubini--Lebesgue":[87],"theorem,":[88],"which":[89,125],"yields":[90],"an":[91],"identification":[92,111,119],"with":[100],"space":[106],"curves.":[109],"then":[115],"enables":[116],"similar":[118],"curves,":[123],"from":[124],"follows.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-03-12T00:00:00"}