{"id":"https://openalex.org/W7214044985","doi":"https://doi.org/10.48550/arxiv.2609.23544","title":"Robin eigenvalue ratios: monotonicity on boxes and counterexamples","display_name":"Robin eigenvalue ratios: monotonicity on boxes and counterexamples","publication_year":2026,"publication_date":"2026-09-20","ids":{"openalex":"https://openalex.org/W7214044985","doi":"https://doi.org/10.48550/arxiv.2609.23544"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.23544","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23544","pdf_url":"https://arxiv.org/pdf/2609.23544","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/2609.23544","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152480613","display_name":"Guowei Dai","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dai, Guowei","raw_affiliation_strings":["Research","School of Mathematical Sciences , Dalian University of Technology , Dalian , 116024 , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research","institution_ids":[]},{"raw_affiliation_string":"School of Mathematical Sciences , Dalian University of Technology , Dalian , 116024 , P.R. China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108975359","display_name":"Yingxin Sun","orcid":"https://orcid.org/0009-0007-0628-4955","observed_orcids":["https://orcid.org/0009-0007-0628-4955"]},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sun, Yingxin","raw_affiliation_strings":["School of Mathematical Sciences , Dalian University of Technology , Dalian , 116024 , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Dalian University of Technology , Dalian , 116024 , P.R. China","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27357992"],"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":0.9961000084877014,"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":0.9961000084877014,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.000699999975040555,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0003000000142492354,"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/eigenvalue-ratio","display_name":"eigenvalue ratio","score":0.6330000162124634},{"id":"https://openalex.org/keywords/monotonicity","display_name":"monotonicity","score":0.7279999852180481},{"id":"https://openalex.org/keywords/polyhedral-domains","display_name":"polyhedral domains","score":0.7839999794960022},{"id":"https://openalex.org/keywords/rectangular-box","display_name":"rectangular box","score":0.9520000219345093},{"id":"https://openalex.org/keywords/polygonal-domains","display_name":"polygonal domains","score":0.7269999980926514},{"id":"https://openalex.org/keywords/neumann-laplacian","display_name":"Neumann Laplacian","score":0.5590000152587891}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.8549000024795532},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.847100019454956},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7250999808311462},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.7110000252723694},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.669700026512146},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6011000275611877},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.597100019454956},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5940999984741211},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5674999952316284},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5537999868392944},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5015000104904175},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C167204820","wikidata":"https://www.wikidata.org/wiki/Q912058","display_name":"Simply connected space","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2603999972343445}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.23544","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23544","pdf_url":"https://arxiv.org/pdf/2609.23544","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.2609.23544","doi":"https://doi.org/10.48550/arxiv.2609.23544","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.23544","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.23544","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23544","pdf_url":"https://arxiv.org/pdf/2609.23544","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":[{"id":"https://openalex.org/G4772512679","display_name":null,"funder_award_id":"12371110","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214044985.pdf","grobid_xml":"https://content.openalex.org/works/W7214044985.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4416781988"],"related_works":["https://openalex.org/W4416781988","https://openalex.org/W7097207377","https://openalex.org/W2966498828","https://openalex.org/W1799060895","https://openalex.org/W6910538697","https://openalex.org/W2945418470","https://openalex.org/W4414273005","https://openalex.org/W2048730655","https://openalex.org/W2804144756","https://openalex.org/W2738673937"],"abstract_inverted_index":{"We":[0],"disprove":[1],"Laugesen's":[2],"conjecture":[3],"that":[4],"the":[5,8,15,27,45,47,72],"ratio":[6,28],"of":[7,24,71,75],"first":[9],"two":[10],"Robin":[11],"eigenvalues":[12],"decreases":[13],"with":[14],"positive":[16,25],"boundary":[17],"parameter.":[18],"On":[19],"any":[20],"prescribed":[21],"compact":[22],"interval":[23,76],"parameters,":[26],"is":[29],"strictly":[30],"increasing":[31],"on":[32,61],"a":[33,51,69],"suitable":[34],"connected":[35,53],"polyhedral":[36],"domain":[37,48],"in":[38,44],"every":[39,62],"dimension":[40],"at":[41],"least":[42],"two;":[43],"plane,":[46],"can":[49],"be":[50],"simply":[52],"polygon.":[54],"In":[55],"contrast,":[56],"we":[57],"prove":[58],"strict":[59],"decrease":[60],"rectangular":[63],"box.":[64],"Both":[65],"results":[66],"follow":[67],"from":[68],"comparison":[70],"relative":[73],"growth":[74],"eigenvalues.":[77]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}