{"id":"https://openalex.org/W7224126537","doi":"https://doi.org/10.48550/arxiv.2610.37559","title":"Boundary Plateau Laws I","display_name":"Boundary Plateau Laws I","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7224126537","doi":"https://doi.org/10.48550/arxiv.2610.37559"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.37559","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37559","pdf_url":"https://arxiv.org/pdf/2610.37559","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/2610.37559","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082837579","display_name":"Camillo De Lellis","orcid":"https://orcid.org/0000-0002-4089-7129","observed_orcids":["https://orcid.org/0000-0002-4089-7129"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"De Lellis, Camillo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001839288","display_name":"Federico Glaudo","orcid":"https://orcid.org/0009-0004-1243-0515","observed_orcids":["https://orcid.org/0009-0004-1243-0515"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Glaudo, Federico","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":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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":9.999999747378752e-05,"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/plateau-s-problem","display_name":"Plateau problem","score":0.7990000247955322},{"id":"https://openalex.org/keywords/soap-films","display_name":"soap films","score":0.7839999794960022}],"concepts":[{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.597100019454956},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.5382999777793884},{"id":"https://openalex.org/C2780030769","wikidata":"https://www.wikidata.org/wiki/Q4968575","display_name":"Plateau (mathematics)","level":2,"score":0.5360999703407288},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5090000033378601},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4185999929904938},{"id":"https://openalex.org/C2993043157","wikidata":"https://www.wikidata.org/wiki/Q4949967","display_name":"Boundary line","level":2,"score":0.3961000144481659},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.37299999594688416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36169999837875366},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.3260999917984009},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3095000088214874},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2678999900817871}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.37559","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37559","pdf_url":"https://arxiv.org/pdf/2610.37559","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.2610.37559","doi":"https://doi.org/10.48550/arxiv.2610.37559","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.37559","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:2610.37559","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37559","pdf_url":"https://arxiv.org/pdf/2610.37559","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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224126537.pdf","grobid_xml":"https://content.openalex.org/works/W7224126537.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7224091034","https://openalex.org/W1964922171","https://openalex.org/W2058788038","https://openalex.org/W7221861069","https://openalex.org/W2615943640","https://openalex.org/W2042267347","https://openalex.org/W2050121173","https://openalex.org/W2093494429","https://openalex.org/W1647798013","https://openalex.org/W2122213968"],"abstract_inverted_index":{"We":[0],"give":[1],"a":[2,23],"complete":[3],"list":[4],"of":[5,10],"the":[6,16],"possible":[7],"local":[8],"shapes":[9],"soap":[11],"films":[12],"where":[13],"they":[14],"wet":[15],"whole":[17],"wire.":[18],"In":[19],"rigorous":[20],"terms,":[21],"given":[22],"straight":[24],"line":[25],"$\\ell":[26],"\\subset":[27],"\\mathbb":[28],"R^3$,":[29],"we":[30],"study":[31],"$2$-dimensional":[32],"cones":[33],"in":[34],"$\\mathbb":[35],"R^3$":[36],"which":[37],"contain":[38],"$\\ell$":[39],"and":[40],"are":[41],"Almgren":[42],"minimizing":[43],"with":[44],"respect":[45],"to":[46],"$\\ell$.":[47]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-29T00:00:00"}