{"id":"https://openalex.org/W4405034967","doi":"https://doi.org/10.48550/arxiv.2412.01510","title":"Minimal Submanifolds and Waists of Locally Symmetric Spaces","display_name":"Minimal Submanifolds and Waists of Locally Symmetric Spaces","publication_year":2024,"publication_date":"2024-12-02","ids":{"openalex":"https://openalex.org/W4405034967","doi":"https://doi.org/10.48550/arxiv.2412.01510"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2412.01510","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2412.01510","pdf_url":"https://arxiv.org/pdf/2412.01510","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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/2412.01510","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018362756","display_name":"Miko\u0142aj Fr\u0105czyk","orcid":"https://orcid.org/0000-0002-6780-2548","observed_orcids":["https://orcid.org/0000-0002-6780-2548"]},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Fraczyk, Mikolaj","raw_affiliation_strings":["Faculty of Mathematics and Computer Science , Jagiellonian University , ul. \u0141o- jasiewicza 6 , 30-348 Krak\u00f3w , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science , Jagiellonian University , ul. \u0141o- jasiewicza 6 , 30-348 Krak\u00f3w , Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110986410","display_name":"Ben Lowe","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lowe, Ben","raw_affiliation_strings":["Department of Mathematics , University of Chicago , Chicago , IL 60637"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Chicago , Chicago , IL 60637","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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":0.5659000277519226,"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":0.5659000277519226,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.36230000853538513,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.03550000116229057,"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/minimal-submanifolds","display_name":"minimal submanifolds","score":0.9850000143051147},{"id":"https://openalex.org/keywords/waist","display_name":"waist","score":0.7260000109672546},{"id":"https://openalex.org/keywords/locally-symmetric-spaces","display_name":"locally symmetric spaces","score":0.8880000114440918},{"id":"https://openalex.org/keywords/sl-n-r","display_name":"SL(n,R)","score":0.6930000185966492},{"id":"https://openalex.org/keywords/monotonicity-formula","display_name":"monotonicity formula","score":0.9039999842643738},{"id":"https://openalex.org/keywords/matrix-coefficients","display_name":"matrix coefficients","score":0.871999979019165},{"id":"https://openalex.org/keywords/unitary-representations","display_name":"unitary representations","score":0.953000009059906}],"concepts":[{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5092359781265259},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49959492683410645},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32193654775619507}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2412.01510","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2412.01510","pdf_url":"https://arxiv.org/pdf/2412.01510","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:arXiv.org:2609.40200","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.40200","pdf_url":"https://arxiv.org/pdf/2609.40200","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.2412.01510","doi":"https://doi.org/10.48550/arxiv.2412.01510","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2412.01510","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.48550/arxiv.2609.40200","doi":"https://doi.org/10.48550/arxiv.2609.40200","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.40200","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2412.01510","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2412.01510","pdf_url":"https://arxiv.org/pdf/2412.01510","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405034967.pdf","grobid_xml":"https://content.openalex.org/works/W4405034967.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1481370475","https://openalex.org/W1937828932","https://openalex.org/W4322618918","https://openalex.org/W4385848612","https://openalex.org/W4391940616","https://openalex.org/W4396600073","https://openalex.org/W4396816419","https://openalex.org/W4407127860","https://openalex.org/W4416891287","https://openalex.org/W7106805182","https://openalex.org/W7204274351","https://openalex.org/W7214005993"],"related_works":["https://openalex.org/W2266362692","https://openalex.org/W7099601562","https://openalex.org/W2360534577","https://openalex.org/W2566572535","https://openalex.org/W1986273152","https://openalex.org/W2097176584","https://openalex.org/W2046329774","https://openalex.org/W7160934253","https://openalex.org/W1574965415","https://openalex.org/W7002197163"],"abstract_inverted_index":{"We":[0,18,71,90,153],"study":[1],"the":[2,39,42,62,105,117],"higher":[3],"expansion":[4],"properties":[5],"of":[6,25,41,67,79,98,107,121,151,176],"locally":[7,28,64,135],"symmetric":[8,29,65,136],"spaces,":[9],"with":[10],"a":[11,46,86,112,126,156,171,185],"particular":[12],"focus":[13],"on":[14,116,170],"octonionic":[15,27,54,99,122],"hyperbolic":[16,55,100,123],"manifolds.":[17,124],"show":[19,73,154],"that":[20,74,95,132,158],"codimension":[21,58,76],"two":[22,59,77],"minimal":[23],"submanifolds":[24],"compact":[26],"spaces":[30,137,142],"must":[31],"have":[32,163],"large":[33,149],"volume,":[34],"at":[35,178],"least":[36],"linear":[37,50],"in":[38,57,104,161],"volume":[40,81],"ambient":[43],"space.":[44],"As":[45],"corollary":[47],"we":[48,130],"prove":[49,94,131],"waist":[51],"inequalities":[52],"for":[53],"manifolds":[56,101],"and":[60,109],"construct":[61],"first":[63],"examples":[66],"power-law":[68],"systolic":[69],"freedom.":[70],"also":[72],"any":[75,168],"submanifold":[78],"small":[80],"can":[82],"be":[83],"homotoped":[84],"to":[85,93,110,138],"lower":[87,114],"dimensional":[88,140],"set.":[89],"use":[91],"this":[92],"branched":[96],"covers":[97],"are":[102],"stable":[103],"sense":[106],"Dinur-Meshulam":[108],"establish":[111],"uniform":[113],"bound":[115],"non-abelian":[118],"Cheeger":[119],"constants":[120],"In":[125],"more":[127],"general":[128],"setting,":[129],"maps":[133],"from":[134],"low":[139],"euclidean":[141],"admit":[143],"fibers":[144],"whose":[145],"fundamental":[146],"group":[147],"has":[148,184],"exponent":[150],"growth.":[152],"as":[155],"consequence":[157],"cocompact":[159],"lattices":[160],"$SL_n(\\mathbb{R})$":[162],"property":[164],"$":[165,180],"FA_{\\lfloor":[166],"n/8\\rfloor-1}$:":[167],"action":[169],"contractible":[172],"$CAT(0)$":[173],"simplicial":[174],"complex":[175],"dimension":[177],"most":[179],"\\lfloor":[181],"n/8\\rfloor":[182],"-1$":[183],"global":[186],"fixed":[187],"point.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2024-12-05T00:00:00"}