{"id":"https://openalex.org/W7212068932","doi":"https://doi.org/10.48550/arxiv.2609.06299","title":"Lifting curved Kakeya sets to linear Kakeya sets","display_name":"Lifting curved Kakeya sets to linear Kakeya sets","publication_year":2026,"publication_date":"2026-09-05","ids":{"openalex":"https://openalex.org/W7212068932","doi":"https://doi.org/10.48550/arxiv.2609.06299"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.06299","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06299","pdf_url":"https://arxiv.org/pdf/2609.06299","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/2609.06299","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009860505","display_name":"Arian Nadjimzadah","orcid":"https://orcid.org/0000-0003-0174-3271","observed_orcids":["https://orcid.org/0000-0003-0174-3271"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nadjimzadah, Arian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5009860505"],"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.98580002784729,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.98580002784729,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.004600000102072954,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0032999999821186066,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/quadratic-curves","display_name":"quadratic curves","score":0.8019999861717224}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8198999762535095},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8184000253677368},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.6844000220298767},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5813000202178955},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5580999851226807},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4643000066280365},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45210000872612},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.40450000762939453},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39640000462532043},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3084999918937683},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2793999910354614},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.2653000056743622},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26420000195503235},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.2606000006198883}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.06299","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06299","pdf_url":"https://arxiv.org/pdf/2609.06299","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.2609.06299","doi":"https://doi.org/10.48550/arxiv.2609.06299","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.06299","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:2609.06299","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06299","pdf_url":"https://arxiv.org/pdf/2609.06299","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/W7212068932.pdf","grobid_xml":"https://content.openalex.org/works/W7212068932.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4416716583"],"related_works":["https://openalex.org/W3102988705","https://openalex.org/W2224336833","https://openalex.org/W7077870763","https://openalex.org/W4415286299","https://openalex.org/W4416365652","https://openalex.org/W2059301084","https://openalex.org/W2951647673","https://openalex.org/W4225990594","https://openalex.org/W7095912068","https://openalex.org/W7158770607"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,116],"many":[3],"curved":[4,42,70,130],"Kakeya":[5,18,29,43,71,78,88,119,131],"problems,":[6],"originally":[7],"motivated":[8],"by":[9,97,109],"H\u00f6rmander's":[10],"oscillatory":[11],"integral":[12],"problem,":[13],"lift":[14],"to":[15,57],"the":[16,27,37,58,76,117],"classical":[17,28,118],"problem":[19],"in":[20,34,55,121,133],"higher":[21],"dimensions.":[22,135],"As":[23],"a":[24,65,83,102,106,126],"consequence,":[25],"if":[26],"set":[30,79],"conjecture":[31,80,120],"were":[32],"true":[33],"all":[35],"dimensions,":[36],"families":[38],"of":[39,87,90,105,129],"curves":[40],"whose":[41],"sets":[44,89],"have":[45],"full":[46],"dimension":[47],"are":[48],"dense":[49,60],"among":[50],"H\u00f6rmander-type":[51],"families.":[52],"This":[53],"is":[54,64],"contrast":[56],"nowhere":[59],"Bourgain's":[61],"condition,":[62],"which":[63],"necessary":[66],"condition":[67],"for":[68],"best-case":[69],"maximal":[72],"function":[73],"estimates.":[74],"Furthermore":[75],"linear":[77],"would":[81],"imply":[82],"fairly":[84],"complete":[85],"understanding":[86,104],"quadratic":[91],"curves,":[92],"as":[93],"first":[94],"studied":[95],"systematically":[96],"Wisewell.":[98],"These":[99],"results":[100],"give":[101],"better":[103],"question":[107],"posed":[108],"Guo--Guth--Nadjimzadah--Shen--Zhang,":[110],"and":[111],"they":[112],"more":[113],"generally":[114],"show":[115],"high":[122],"dimensions":[123],"rests":[124],"on":[125],"broad":[127],"range":[128],"problems":[132],"lower":[134]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}