{"id":"https://openalex.org/W7213908416","doi":"https://doi.org/10.48550/arxiv.2609.21326","title":"Sharp bounds for higher mixed Steklov-Robin eigenvalues on domains with holes","display_name":"Sharp bounds for higher mixed Steklov-Robin eigenvalues on domains with holes","publication_year":2026,"publication_date":"2026-09-18","ids":{"openalex":"https://openalex.org/W7213908416","doi":"https://doi.org/10.48550/arxiv.2609.21326"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.21326","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21326","pdf_url":"https://arxiv.org/pdf/2609.21326","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/2609.21326","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076188660","display_name":"Sagar Basak","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Basak, Sagar","raw_affiliation_strings":["Department of Mathematical Sciences , Indian Institute of Technology (BHU) , Varanasi , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Indian Institute of Technology (BHU) , Varanasi , India","institution_ids":["https://openalex.org/I56404289"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076188660"],"corresponding_institution_ids":["https://openalex.org/I56404289"],"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":0.9824000000953674,"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":0.9824000000953674,"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":0.003700000001117587,"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":0.0020000000949949026,"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/higher-eigenvalues","display_name":"higher eigenvalues","score":0.6840000152587891},{"id":"https://openalex.org/keywords/isoperimetric-inequality","display_name":"isoperimetric inequality","score":0.9020000100135803},{"id":"https://openalex.org/keywords/domains-with-holes","display_name":"domains with holes","score":0.8320000171661377},{"id":"https://openalex.org/keywords/lipschitz-domains","display_name":"Lipschitz domains","score":0.8550000190734863}],"concepts":[{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.9075999855995178},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.755299985408783},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7524999976158142},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.717199981212616},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5605000257492065},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5194000005722046},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4643000066280365},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.4505999982357025},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4142000079154968},{"id":"https://openalex.org/C70266181","wikidata":"https://www.wikidata.org/wiki/Q3707726","display_name":"Isoperimetric dimension","level":3,"score":0.30320000648498535},{"id":"https://openalex.org/C20892832","wikidata":"https://www.wikidata.org/wiki/Q3271879","display_name":"Circular symmetry","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.271699994802475},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C28940832","wikidata":"https://www.wikidata.org/wiki/Q3490774","display_name":"Spectrum of a matrix","level":4,"score":0.2596000134944916},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.2572000026702881},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.21326","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21326","pdf_url":"https://arxiv.org/pdf/2609.21326","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.2609.21326","doi":"https://doi.org/10.48550/arxiv.2609.21326","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.21326","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:2609.21326","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21326","pdf_url":"https://arxiv.org/pdf/2609.21326","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":[{"id":"https://openalex.org/F4320320767","display_name":"University Grants Commission","ror":"https://ror.org/04p800546"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213908416.pdf","grobid_xml":"https://content.openalex.org/works/W7213908416.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W3043489982","https://openalex.org/W7141115333"],"related_works":["https://openalex.org/W4416842563","https://openalex.org/W4405767404","https://openalex.org/W7141115333","https://openalex.org/W7202165608","https://openalex.org/W4390629892","https://openalex.org/W3019215484","https://openalex.org/W2907922275","https://openalex.org/W3083517475","https://openalex.org/W2951812898","https://openalex.org/W4320853711"],"abstract_inverted_index":{"This":[0],"article":[1],"is":[2],"concerned":[3],"with":[4,16,23],"mixed":[5],"Steklov--Robin":[6],"eigenvalues":[7,40],"on":[8,60],"bounded":[9],"domains":[10,22,64],"in":[11],"$\\mathbb{R}^{n},":[12],"n":[13],"\\geq":[14],"2$,":[15],"Lipschitz":[17],"boundary.":[18],"Specifically,":[19],"we":[20],"consider":[21],"symmetry":[24,58],"of":[25,63],"order":[26],"$4$":[27],"containing":[28],"a":[29],"spherical":[30],"hole.":[31],"We":[32,49],"obtain":[33],"isoperimetric":[34],"inequalities":[35],"for":[36,41],"the":[37,54,57,61],"$k$-th":[38],"Steklov-Robin":[39],"each":[42],"$k":[43],"\\in":[44],"\\{2,":[45],"3,":[46],"\\dots,":[47],"n+1\\}$.":[48],"provide":[50],"examples":[51],"to":[52],"emphasize":[53],"fact":[55],"that":[56],"assumptions,":[59],"family":[62],"considered,":[65],"are":[66],"crucial.":[67]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-22T00:00:00"}