{"id":"https://openalex.org/W7222465591","doi":"https://doi.org/10.48550/arxiv.2610.21417","title":"A quantitative Robin P\u00f3lya--Szeg\u0151 theorem for tangential polygons","display_name":"A quantitative Robin P\u00f3lya--Szeg\u0151 theorem for tangential polygons","publication_year":2026,"publication_date":"2026-10-15","ids":{"openalex":"https://openalex.org/W7222465591","doi":"https://doi.org/10.48550/arxiv.2610.21417"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.21417","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.21417","pdf_url":"https://arxiv.org/pdf/2610.21417","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/2610.21417","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125382470","display_name":"Changfeng Gui","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gui, Changfeng","raw_affiliation_strings":["School of Mathematics , Hunan University , Changsha , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Hunan University , Changsha , P.R. China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017630999","display_name":"Yeyao Hu","orcid":"https://orcid.org/0000-0002-0910-9577","observed_orcids":["https://orcid.org/0000-0002-0910-9577","https://orcid.org/0009-0005-9565-5281"]},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hu, Yeyao","raw_affiliation_strings":["School of Mathematics , Hunan University , Changsha , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Hunan University , Changsha , P.R. China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5158910788","display_name":"Qinfeng Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Qinfeng","raw_affiliation_strings":["School of Mathematics , Hunan University , Changsha , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Hunan University , Changsha , P.R. China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5158898125","display_name":"Hang Yang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang, Hang","raw_affiliation_strings":["School of Mathematics , Hunan University , Changsha , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Hunan University , Changsha , P.R. China","institution_ids":["https://openalex.org/I16609230"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I16609230"],"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":0.8192999958992004,"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":0.8192999958992004,"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":0.06989999860525131,"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":0.035100001841783524,"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/regular-polygons","display_name":"regular polygons","score":0.7760000228881836},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.8100000023841858},{"id":"https://openalex.org/keywords/isoperimetric-inequality","display_name":"isoperimetric inequality","score":0.6420000195503235},{"id":"https://openalex.org/keywords/robin-boundary-conditions","display_name":"Robin boundary conditions","score":0.4050000011920929},{"id":"https://openalex.org/keywords/neumann-boundary-conditions","display_name":"Neumann boundary conditions","score":0.800000011920929},{"id":"https://openalex.org/keywords/spectral-estimates","display_name":"spectral estimates","score":0.6269999742507935},{"id":"https://openalex.org/keywords/triangles","display_name":"triangles","score":0.47099998593330383}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8503999710083008},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.5611000061035156},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.555899977684021},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5235999822616577},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.48350000381469727},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.41499999165534973},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.36660000681877136},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35010001063346863},{"id":"https://openalex.org/C98503990","wikidata":"https://www.wikidata.org/wiki/Q28474","display_name":"Perimeter","level":2,"score":0.3409999907016754},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.3253999948501587},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27320000529289246},{"id":"https://openalex.org/C102231394","wikidata":"https://www.wikidata.org/wiki/Q5280763","display_name":"Dirichlet eigenvalue","level":5,"score":0.2712000012397766},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.26010000705718994}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.21417","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.21417","pdf_url":"https://arxiv.org/pdf/2610.21417","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.2610.21417","doi":"https://doi.org/10.48550/arxiv.2610.21417","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.21417","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:2610.21417","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.21417","pdf_url":"https://arxiv.org/pdf/2610.21417","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/W7222465591.pdf","grobid_xml":"https://content.openalex.org/works/W7222465591.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W44035921","https://openalex.org/W227029647","https://openalex.org/W562484954","https://openalex.org/W2089422038","https://openalex.org/W2125703826","https://openalex.org/W2147822028","https://openalex.org/W2183710234","https://openalex.org/W2564087643","https://openalex.org/W3035686769","https://openalex.org/W3092448016","https://openalex.org/W3093394262","https://openalex.org/W3112400970","https://openalex.org/W3134755024","https://openalex.org/W3165788428","https://openalex.org/W3186669935","https://openalex.org/W4318476256","https://openalex.org/W4322625404","https://openalex.org/W4395485011","https://openalex.org/W4403624409","https://openalex.org/W4416344054","https://openalex.org/W4417081724","https://openalex.org/W7094184820","https://openalex.org/W7133847644","https://openalex.org/W7143340295","https://openalex.org/W7163026319","https://openalex.org/W7164477794","https://openalex.org/W7172341765"],"related_works":["https://openalex.org/W7172341765","https://openalex.org/W7164477794","https://openalex.org/W7214057587","https://openalex.org/W3134755024","https://openalex.org/W7213523160","https://openalex.org/W3112400970","https://openalex.org/W2067915597","https://openalex.org/W4304544052","https://openalex.org/W3164305663","https://openalex.org/W4399405636"],"abstract_inverted_index":{"We":[0,82],"extend":[1],"the":[2,23,43,69,92],"quantitative":[3,119],"Dirichlet":[4,44],"theorem":[5],"of":[6,34,94],"Gui,":[7,48],"Hu,":[8,49],"and":[9,50,53,78,117],"Li":[10,51],"\\cite{GuiHuLi2026}":[11,52],"to":[12],"Robin":[13,28,56],"torsional":[14,29],"rigidity.":[15],"For":[16,65],"every":[17],"fixed":[18],"$\u03b2>0$,":[19],"we":[20,67],"prove":[21],"that":[22,58],"regular":[24,89],"$N$-gon":[25],"uniquely":[26],"maximizes":[27],"rigidity":[30],"among":[31],"tangential":[32,63],"$N$-gons":[33],"prescribed":[35],"area.":[36],"Our":[37],"explicit":[38,99],"perimeter":[39],"deficit":[40,45],"bound":[41,100],"contains":[42],"obtained":[46],"by":[47,76],"an":[54,98],"additional":[55],"term":[57],"is":[59],"positive":[60],"for":[61,101,114],"nonregular":[62],"polygons.":[64],"triangles,":[66],"answer":[68],"fixed-area":[70],"optimization":[71],"problem":[72],"recorded":[73],"as":[74,91],"open":[75],"Keady":[77],"Wiwatanapataphee":[79],"\\cite[Appendix":[80],"A.1.2]{KeadyWiwatanapataphee2016}.":[81],"also":[83],"establish":[84],"strict":[85],"monotonicity":[86],"along":[87],"equal-area":[88],"polygons":[90],"number":[93],"sides":[95],"increases,":[96],"with":[97],"each":[102],"consecutive":[103],"gap.":[104],"The":[105],"proof":[106],"combines":[107],"mixed":[108],"Robin--Neumann":[109],"triangular":[110],"cells,":[111],"spectral":[112],"estimates":[113],"angular":[115],"concavity,":[116],"a":[118],"scaling":[120],"estimate.":[121]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-17T00:00:00"}
