{"id":"https://openalex.org/W7221833995","doi":"https://doi.org/10.48550/arxiv.2610.16485","title":"A geometric lower bound for the clamped plate eigenvalue problem in low dimensions and extensions","display_name":"A geometric lower bound for the clamped plate eigenvalue problem in low dimensions and extensions","publication_year":2026,"publication_date":"2026-10-12","ids":{"openalex":"https://openalex.org/W7221833995","doi":"https://doi.org/10.48550/arxiv.2610.16485"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.16485","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16485","pdf_url":"https://arxiv.org/pdf/2610.16485","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/2610.16485","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107950684","display_name":"Francesca Bianchi","orcid":"https://orcid.org/0000-0002-4537-7317","observed_orcids":["https://orcid.org/0000-0002-4537-7317"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bianchi, Francesca","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093743379","display_name":"Francesco Bozzola","orcid":"https://orcid.org/0000-0001-6197-5803","observed_orcids":["https://orcid.org/0000-0001-6197-5803"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bozzola, Francesco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006763979","display_name":"Lorenzo Brasco","orcid":"https://orcid.org/0000-0001-5694-7306","observed_orcids":["https://orcid.org/0000-0001-5694-7306"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brasco, Lorenzo","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":0.9599999785423279,"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":0.9599999785423279,"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":0.02319999970495701,"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":0.00430000014603138,"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/inradius","display_name":"inradius","score":0.9470000267028809},{"id":"https://openalex.org/keywords/fractional-laplacian","display_name":"fractional Laplacian","score":0.8090000152587891},{"id":"https://openalex.org/keywords/spectral-bounds","display_name":"spectral bounds","score":0.40299999713897705},{"id":"https://openalex.org/keywords/low-dimensions","display_name":"low dimensions","score":0.335999995470047}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7333999872207642},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7125999927520752},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6766999959945679},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5800999999046326},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5404000282287598},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5335000157356262},{"id":"https://openalex.org/C97787015","wikidata":"https://www.wikidata.org/wiki/Q10615255","display_name":"Incircle and excircles of a triangle","level":2,"score":0.4722000062465668},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.4699999988079071},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46140000224113464},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.3253999948501587},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.31610000133514404},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30799999833106995},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3061999976634979},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2973000109195709},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.2953999936580658},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.25540000200271606}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.16485","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16485","pdf_url":"https://arxiv.org/pdf/2610.16485","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.2610.16485","doi":"https://doi.org/10.48550/arxiv.2610.16485","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.16485","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:2610.16485","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16485","pdf_url":"https://arxiv.org/pdf/2610.16485","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/G2971504390","display_name":null,"funder_award_id":"E53C25002010001","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G364684122","display_name":null,"funder_award_id":"FAR2024","funder_id":"https://openalex.org/F4320324162","funder_display_name":"Universit\u00e0 degli Studi di Ferrara"},{"id":"https://openalex.org/G5153289039","display_name":null,"funder_award_id":"E53C25002010001","funder_id":"https://openalex.org/F4320333369","funder_display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni"},{"id":"https://openalex.org/G5971865997","display_name":"Grupo de F\u00edsica Matem\u00e1tica","funder_award_id":"UID/00208/2025","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320323642","display_name":"Minist\u00e9rio da Ci\u00eancia, Tecnologia e Ensino Superior","ror":"https://ror.org/045b9pr88"},{"id":"https://openalex.org/F4320324162","display_name":"Universit\u00e0 degli Studi di Ferrara","ror":"https://ror.org/041zkgm14"},{"id":"https://openalex.org/F4320333369","display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","ror":"https://ror.org/02ktjph70"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221833995.pdf","grobid_xml":"https://content.openalex.org/works/W7221833995.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3101342926","https://openalex.org/W4386485623","https://openalex.org/W1982983242","https://openalex.org/W851435890","https://openalex.org/W7213422964","https://openalex.org/W2086630663","https://openalex.org/W2023405402","https://openalex.org/W7098565746","https://openalex.org/W4399115553","https://openalex.org/W2950479344"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"the":[3,6,17,31,44],"spectrum":[4],"of":[5,16,43],"Dirichlet-biLaplacian":[7],"can":[8],"be":[9],"quantitatively":[10],"bounded":[11],"from":[12],"below":[13],"in":[14,25],"terms":[15],"inradius":[18],"only,":[19],"for":[20],"a":[21],"general":[22],"open":[23],"set":[24],"dimensions":[26],"$2$":[27],"and":[28],"$3$.":[29],"For":[30],"same":[32],"dimensions,":[33],"we":[34],"also":[35],"extend":[36],"this":[37],"result":[38],"to":[39],"fractional":[40],"powers":[41],"$s$":[42],"Laplacian,":[45],"with":[46],"$N/2":[47]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-15T00:00:00"}