{"id":"https://openalex.org/W7214702276","doi":"https://doi.org/10.48550/arxiv.2609.32946","title":"The relative isoperimetric profile of a unit square with a central square removed","display_name":"The relative isoperimetric profile of a unit square with a central square removed","publication_year":2026,"publication_date":"2026-09-26","ids":{"openalex":"https://openalex.org/W7214702276","doi":"https://doi.org/10.48550/arxiv.2609.32946"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.32946","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32946","pdf_url":"https://arxiv.org/pdf/2609.32946","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/2609.32946","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002878692","display_name":"Kyle Byassee","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Byassee, Kyle","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153481835","display_name":"Hunter Johnson","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Johnson, Hunter","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153485342","display_name":"Brandon Jones","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jones, Brandon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023623567","display_name":"Ezra Nance","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nance, Ezra","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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9800000190734863,"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"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9800000190734863,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.013000000268220901,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/isoperimetric-inequality","display_name":"isoperimetric inequality","score":0.8629999756813049},{"id":"https://openalex.org/keywords/unit-square","display_name":"unit square","score":0.7239999771118164},{"id":"https://openalex.org/keywords/shape-optimization","display_name":"shape optimization","score":0.4659999907016754}],"concepts":[{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.8410999774932861},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.7979999780654907},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.7906000018119812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6194999814033508},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.48420000076293945},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44429999589920044},{"id":"https://openalex.org/C2988709989","wikidata":"https://www.wikidata.org/wiki/Q85784623","display_name":"Mean square","level":2,"score":0.4113999903202057},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4023999869823456},{"id":"https://openalex.org/C98503990","wikidata":"https://www.wikidata.org/wiki/Q28474","display_name":"Perimeter","level":2,"score":0.3937000036239624},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35040000081062317},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C70266181","wikidata":"https://www.wikidata.org/wiki/Q3707726","display_name":"Isoperimetric dimension","level":3,"score":0.3312000036239624},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27239999175071716}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.32946","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32946","pdf_url":"https://arxiv.org/pdf/2609.32946","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.2609.32946","doi":"https://doi.org/10.48550/arxiv.2609.32946","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.32946","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.32946","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32946","pdf_url":"https://arxiv.org/pdf/2609.32946","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/G4648870347","display_name":"Louis Stokes New STEM Pathways Implementation-Only Alliance: The Tennessee Valley Tri-State LSAMP Alliance-Creating a Pathway of Success for General STEM Education","funder_award_id":"2308688","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214702276.pdf","grobid_xml":"https://content.openalex.org/works/W7214702276.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7162312167"],"related_works":["https://openalex.org/W3215586222","https://openalex.org/W7162312167","https://openalex.org/W2168478418","https://openalex.org/W7221810406","https://openalex.org/W7096534977","https://openalex.org/W4320342387","https://openalex.org/W595120184","https://openalex.org/W7095438980","https://openalex.org/W2797190491","https://openalex.org/W4316340007"],"abstract_inverted_index":{"We":[0],"calculate":[1],"the":[2,6,37],"exact":[3],"values":[4],"of":[5,27],"relative":[7,39],"isoperimetric":[8],"profile":[9],"for":[10],"a":[11,15,23,28,33],"unit":[12],"square":[13,17,26],"with":[14],"central":[16,25],"removed.":[18],"In":[19],"other":[20],"words,":[21],"given":[22],"removed":[24],"fixed":[29],"size,":[30],"we":[31],"provide":[32],"function":[34],"which":[35,41],"produces":[36],"smallest":[38],"perimeter":[40],"bounds":[42],"any":[43],"possible":[44],"area":[45],"within":[46],"this":[47],"shape.":[48]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}