{"id":"https://openalex.org/W7214716520","doi":"https://doi.org/10.48550/arxiv.2609.31856","title":"Eigenfunction asymptotics and nodal domain estimates for dumbbell domains","display_name":"Eigenfunction asymptotics and nodal domain estimates for dumbbell domains","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214716520","doi":"https://doi.org/10.48550/arxiv.2609.31856"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.31856","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31856","pdf_url":"https://arxiv.org/pdf/2609.31856","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/2609.31856","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083001314","display_name":"Thomas Beck","orcid":"https://orcid.org/0000-0003-1133-4551","observed_orcids":["https://orcid.org/0000-0003-1133-4551"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Beck, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034438903","display_name":"Yaiza Canzani","orcid":"https://orcid.org/0000-0002-5039-4779","observed_orcids":["https://orcid.org/0000-0002-5039-4779"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Canzani, Yaiza","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055763634","display_name":"Jeremy Louis Marzuola","orcid":"https://orcid.org/0000-0002-8668-7143","observed_orcids":["https://orcid.org/0000-0002-8668-7143"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marzuola, Jeremy L.","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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9990000128746033,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/neumann-eigenfunctions","display_name":"Neumann eigenfunctions","score":0.8820000290870667},{"id":"https://openalex.org/keywords/nodal-domains","display_name":"nodal domains","score":0.9800000190734863},{"id":"https://openalex.org/keywords/eigenfunction-asymptotics","display_name":"eigenfunction asymptotics","score":0.7689999938011169},{"id":"https://openalex.org/keywords/matched-asymptotic-expansions","display_name":"matched asymptotic expansions","score":0.8309999704360962},{"id":"https://openalex.org/keywords/planar-domains","display_name":"planar domains","score":0.7260000109672546}],"concepts":[{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.9124000072479248},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6488000154495239},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6470000147819519},{"id":"https://openalex.org/C83330619","wikidata":"https://www.wikidata.org/wiki/Q21124872","display_name":"NODAL","level":2,"score":0.6284000277519226},{"id":"https://openalex.org/C2776546559","wikidata":"https://www.wikidata.org/wiki/Q465453","display_name":"Dumbbell","level":2,"score":0.5924000144004822},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5741000175476074},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5544999837875366},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.44209998846054077},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.41780000925064087},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.40720000863075256},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.399399995803833},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.39469999074935913},{"id":"https://openalex.org/C138395690","wikidata":"https://www.wikidata.org/wiki/Q376733","display_name":"Cardinal point","level":2,"score":0.367000013589859},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3544999957084656},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.3458999991416931},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27970001101493835},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.27070000767707825}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.31856","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31856","pdf_url":"https://arxiv.org/pdf/2609.31856","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.2609.31856","doi":"https://doi.org/10.48550/arxiv.2609.31856","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.31856","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:2609.31856","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31856","pdf_url":"https://arxiv.org/pdf/2609.31856","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214716520.pdf","grobid_xml":"https://content.openalex.org/works/W7214716520.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4386942409","https://openalex.org/W7125807578"],"related_works":["https://openalex.org/W7125807578","https://openalex.org/W4386942409","https://openalex.org/W4399701693","https://openalex.org/W7150853657","https://openalex.org/W7143532988","https://openalex.org/W2509410836","https://openalex.org/W4301268807","https://openalex.org/W1903100294","https://openalex.org/W4414978534","https://openalex.org/W2017129019"],"abstract_inverted_index":{"We":[0,132],"study":[1],"the":[2,13,16,45,50,53,64,78,93,109,140,145,156],"nodal":[3,42,71,81,125],"structure":[4],"of":[5,15,41,52,83],"Neumann":[6,66,150],"eigenfunctions":[7,97],"on":[8,86,92,114,144],"planar":[9],"dumbbell":[10],"domains":[11,22,43,72,119,126],"as":[12,44],"width":[14],"neck":[17,130,157],"joining":[18],"two":[19],"fixed":[20],"end":[21,88,118],"tends":[23],"to":[24],"zero.":[25],"Under":[26],"simplicity":[27],"and":[28,73,160],"non-degeneracy":[29],"assumptions,":[30],"we":[31],"show":[32],"that":[33,98,108],"sufficiently":[34],"thin":[35],"necks":[36],"force":[37],"an":[38,84,87],"increasing":[39],"number":[40],"limiting":[46],"eigenvalue":[47],"grows.":[48],"At":[49,77],"bottom":[51],"spectrum":[54],"this":[55,134],"forcing":[56],"can":[57,90],"attain":[58],"Courant's":[59],"upper":[60],"bound:":[61],"in":[62],"particular,":[63],"third":[65],"eigenfunction":[67,85],"has":[68],"exactly":[69],"three":[70],"is":[74,107],"Courant":[75,101],"sharp.":[76,102],"same":[79],"time,":[80],"deficiency":[82],"domain":[89],"persist":[91],"full":[94],"dumbbell,":[95],"giving":[96],"are":[99],"not":[100],"The":[103],"main":[104],"analytic":[105],"difficulty":[106],"singular":[110],"limit":[111],"may":[112],"vanish":[113],"one":[115],"or":[116],"both":[117],"even":[120],"though":[121],"these":[122],"regions":[123],"contribute":[124],"for":[127,139],"every":[128],"positive":[129],"width.":[131],"overcome":[133],"by":[135,162],"deriving":[136],"refined":[137],"asymptotics":[138],"first":[141],"nonzero":[142],"profiles":[143],"vanishing":[146],"regions,":[147],"expressed":[148],"through":[149],"Green's":[151],"functions":[152],"with":[153,168],"poles":[154],"at":[155],"attachment":[158],"points":[159],"obtained":[161],"a":[163],"two-dimensional":[164],"matched":[165],"asymptotic":[166],"analysis":[167],"logarithmic":[169],"terms.":[170]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
