{"id":"https://openalex.org/W7221534036","doi":"https://doi.org/10.48550/arxiv.2610.13738","title":"Sharp upper bounds for Steklov eigenvalues on warped products","display_name":"Sharp upper bounds for Steklov eigenvalues on warped products","publication_year":2026,"publication_date":"2026-10-09","ids":{"openalex":"https://openalex.org/W7221534036","doi":"https://doi.org/10.48550/arxiv.2610.13738"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.13738","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13738","pdf_url":"https://arxiv.org/pdf/2610.13738","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/2610.13738","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103181625","display_name":"Jade Brisson","orcid":"https://orcid.org/0000-0003-1434-0877","observed_orcids":["https://orcid.org/0000-0003-1434-0877"]},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Brisson, Jade","raw_affiliation_strings":["Department of Mathematics , King's College London , The Strand , London , WC2R 2LS , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , King's College London , The Strand , London , WC2R 2LS , United Kingdom","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040215890","display_name":"Bruno Colbois","orcid":"https://orcid.org/0000-0002-8514-4315","observed_orcids":["https://orcid.org/0000-0002-8514-4315"]},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Colbois, Bruno","raw_affiliation_strings":["Department of Mathematics , King's College London , The Strand , London , WC2R 2LS , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , King's College London , The Strand , London , WC2R 2LS , United Kingdom","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066917206","display_name":"Alexandre Girouard","orcid":"https://orcid.org/0000-0001-8823-831X","observed_orcids":["https://orcid.org/0000-0001-8823-831X"]},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Girouard, Alexandre","raw_affiliation_strings":["Department of Mathematics , King's College London , The Strand , London , WC2R 2LS , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , King's College London , The Strand , London , WC2R 2LS , United Kingdom","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5158428463","display_name":"Katie Gittins","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Gittins, Katie","raw_affiliation_strings":["Department of Mathematics , King's College London , The Strand , London , WC2R 2LS , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , King's College London , The Strand , London , WC2R 2LS , United Kingdom","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5158530073","display_name":"Jean Lagac\u00e9-Taylor","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Lagac\u00e9-Taylor, Jean","raw_affiliation_strings":["Department of Mathematics , King's College London , The Strand , London , WC2R 2LS , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , King's College London , The Strand , London , WC2R 2LS , United Kingdom","institution_ids":["https://openalex.org/I183935753"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I183935753"],"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":0.98580002784729,"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":0.98580002784729,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.010400000028312206,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/steklov-eigenvalues","display_name":"Steklov eigenvalues","score":1.0},{"id":"https://openalex.org/keywords/warped-products","display_name":"warped products","score":0.9909999966621399},{"id":"https://openalex.org/keywords/weighted-laplacian","display_name":"weighted Laplacian","score":0.753000020980835},{"id":"https://openalex.org/keywords/separation-of-variables","display_name":"separation of variables","score":0.6899999976158142},{"id":"https://openalex.org/keywords/spectral-approximation","display_name":"spectral approximation","score":0.6809999942779541},{"id":"https://openalex.org/keywords/compact-riemannian-manifolds-with-boundary","display_name":"compact Riemannian manifolds with boundary","score":0.824999988079071}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7929999828338623},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.673799991607666},{"id":"https://openalex.org/C51364350","wikidata":"https://www.wikidata.org/wiki/Q3123529","display_name":"Spectral geometry","level":2,"score":0.6000000238418579},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5428000092506409},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5339999794960022},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5260999798774719},{"id":"https://openalex.org/C157202957","wikidata":"https://www.wikidata.org/wiki/Q1659609","display_name":"Image warping","level":2,"score":0.4970000088214874},{"id":"https://openalex.org/C49747540","wikidata":"https://www.wikidata.org/wiki/Q1071846","display_name":"Laplace\u2013Beltrami operator","level":4,"score":0.49140000343322754},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.45489999651908875},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.45399999618530273},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4521999955177307},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44679999351501465},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4041999876499176},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.3991999924182892},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3425999879837036},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.3124000132083893},{"id":"https://openalex.org/C28940832","wikidata":"https://www.wikidata.org/wiki/Q3490774","display_name":"Spectrum of a matrix","level":4,"score":0.30410000681877136},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2865000069141388},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C136005978","wikidata":"https://www.wikidata.org/wiki/Q1362077","display_name":"First variation","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.2615000009536743}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.13738","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13738","pdf_url":"https://arxiv.org/pdf/2610.13738","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.2610.13738","doi":"https://doi.org/10.48550/arxiv.2610.13738","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.13738","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:2610.13738","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13738","pdf_url":"https://arxiv.org/pdf/2610.13738","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/G1210808807","display_name":"Isaac Newton Institute for Mathematical Sciences (INI)","funder_award_id":"EP/Z000580/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4033033583","display_name":null,"funder_award_id":"200021_19689","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G993971353","display_name":null,"funder_award_id":"200021","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221534036.pdf","grobid_xml":"https://content.openalex.org/works/W7221534036.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7116085783","https://openalex.org/W4393063722","https://openalex.org/W2914257966","https://openalex.org/W4401686586","https://openalex.org/W4414333195","https://openalex.org/W2992344789","https://openalex.org/W7117850984","https://openalex.org/W2905099191","https://openalex.org/W2962802576","https://openalex.org/W2069460639"],"abstract_inverted_index":{"We":[0,86],"obtain":[1],"sharp":[2],"isoperimetric-type":[3],"upper":[4],"bounds":[5,28,64],"for":[6],"Steklov":[7,54],"eigenvalues":[8,44,55],"on":[9,49,73,106,120],"warped":[10,34],"products":[11],"whose":[12,21],"bases":[13],"are":[14,23,65,125],"compact":[15],"Riemannian":[16,25],"manifolds":[17,121],"with":[18,69],"boundary":[19],"and":[20,36,52],"fibres":[22,124],"closed":[24],"manifolds.":[26],"These":[27],"involve":[29],"the":[30,33,43,46,50,53,57,74,83,89,98,107,123],"volume":[31],"of":[32,37,45,56,61,91,113],"product":[35],"its":[38],"boundary,":[39],"as":[40,42,97],"well":[41],"Laplace":[47,78],"operator":[48],"fibre":[51],"base.":[58],"After":[59],"separation":[60],"variables,":[62],"these":[63],"obtained":[66],"by":[67,82],"comparison":[68],"auxiliary":[70],"Helmholtz-Steklov":[71],"problems":[72],"base":[75],"involving":[76],"weighted":[77],"operators":[79],"naturally":[80],"induced":[81],"warping":[84,99],"function.":[85],"also":[87],"study":[88],"effect":[90],"various":[92,114],"natural":[93],"geometric":[94],"constraints,":[95],"such":[96],"function":[100],"being":[101],"identically":[102],"equal":[103],"to":[104],"one":[105],"boundary.":[108],"The":[109],"proofs":[110],"make":[111],"use":[112],"spectral":[115],"approximation":[116],"methods,":[117],"including":[118],"homogenisation":[119],"when":[122],"one-dimensional.":[126]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-13T00:00:00"}