{"id":"https://openalex.org/W7220979413","doi":"https://doi.org/10.48550/arxiv.2610.10119","title":"Maximisers for the second Neumann eigenvalue of annuli in two-dimensional space forms","display_name":"Maximisers for the second Neumann eigenvalue of annuli in two-dimensional space forms","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220979413","doi":"https://doi.org/10.48550/arxiv.2610.10119"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10119","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10119","pdf_url":"https://arxiv.org/pdf/2610.10119","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.10119","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035652740","display_name":"Luigi Provenzano","orcid":"https://orcid.org/0000-0002-1804-3725","observed_orcids":["https://orcid.org/0000-0002-1804-3725"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Provenzano, Luigi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5057583131","display_name":"Alessandro Savo","orcid":"https://orcid.org/0000-0001-6236-2160","observed_orcids":["https://orcid.org/0000-0001-6236-2160"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Savo, Alessandro","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":0.9765999913215637,"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":0.9765999913215637,"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":0.01209999993443489,"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":0.005900000222027302,"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-eigenvalues","display_name":"Neumann eigenvalues","score":0.8299999833106995},{"id":"https://openalex.org/keywords/annuli","display_name":"annuli","score":0.7839999794960022},{"id":"https://openalex.org/keywords/space-forms","display_name":"space forms","score":0.8349999785423279},{"id":"https://openalex.org/keywords/sphere","display_name":"sphere","score":0.6050000190734863},{"id":"https://openalex.org/keywords/euclidean-plane","display_name":"Euclidean plane","score":0.8149999976158142},{"id":"https://openalex.org/keywords/hyperbolic-plane","display_name":"hyperbolic plane","score":0.9990000128746033},{"id":"https://openalex.org/keywords/doubly-connected-domains","display_name":"doubly connected domains","score":0.8349999785423279},{"id":"https://openalex.org/keywords/spectral-inequalities","display_name":"spectral inequalities","score":0.367000013589859}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8065000176429749},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7541999816894531},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5995000004768372},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5799000263214111},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5688999891281128},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.430400013923645},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4203000068664551},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.3984000086784363},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.3449999988079071},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.3353999853134155},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2987000048160553},{"id":"https://openalex.org/C137343772","wikidata":"https://www.wikidata.org/wiki/Q584910","display_name":"Neumann series","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.26179999113082886}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10119","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10119","pdf_url":"https://arxiv.org/pdf/2610.10119","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.2610.10119","doi":"https://doi.org/10.48550/arxiv.2610.10119","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10119","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.10119","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10119","pdf_url":"https://arxiv.org/pdf/2610.10119","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/W7220979413.pdf","grobid_xml":"https://content.openalex.org/works/W7220979413.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3127283689","https://openalex.org/W4225535731","https://openalex.org/W4282590150","https://openalex.org/W1549246382","https://openalex.org/W7133758599","https://openalex.org/W2895720969","https://openalex.org/W7095577709","https://openalex.org/W2964069692","https://openalex.org/W4395670058","https://openalex.org/W1586863316"],"abstract_inverted_index":{"We":[0,62],"prove":[1],"a":[2],"sharp":[3],"Szeg\u00f6-Weinberger-type":[4],"inequality":[5,76],"for":[6,57],"balanced":[7],"doubly":[8],"connected":[9],"domains":[10],"in":[11,78],"$\\mathbb":[12,14,17],"S^2$,":[13],"R^2$":[15],"and":[16,44],"H^2$.":[18],"More":[19],"precisely,":[20],"the":[21,32,39,42,45,48,52,58,66,75],"first":[22],"positive":[23],"Neumann":[24],"eigenvalue":[25],"is":[26,69],"bounded":[27],"above":[28],"by":[29,38],"that":[30,65],"of":[31,41,47,51],"corresponding":[33],"rotationally":[34,59],"symmetric":[35,60],"annulus,":[36],"determined":[37],"area":[40,46],"domain":[43],"smallest":[49],"component":[50],"complement.":[53],"Equality":[54],"holds":[55],"only":[56],"annulus.":[61],"also":[63],"show":[64],"balancing":[67],"assumption":[68],"essential:":[70],"if":[71],"we":[72],"drop":[73],"it,":[74],"fails":[77],"general.":[79]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-09T00:00:00"}