{"id":"https://openalex.org/W7213245246","doi":"https://doi.org/10.48550/arxiv.2609.14035","title":"Finite Polyhedral Models for the Space of Equivalent Norms","display_name":"Finite Polyhedral Models for the Space of Equivalent Norms","publication_year":2026,"publication_date":"2026-09-12","ids":{"openalex":"https://openalex.org/W7213245246","doi":"https://doi.org/10.48550/arxiv.2609.14035"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.14035","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14035","pdf_url":"https://arxiv.org/pdf/2609.14035","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/2609.14035","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030143533","display_name":"Juan Rafael Acosta-Portilla","orcid":"https://orcid.org/0000-0002-8063-0752","observed_orcids":["https://orcid.org/0000-0002-8063-0752"]},"institutions":[{"id":"https://openalex.org/I147280213","display_name":"Universidad Veracruzana","ror":"https://ror.org/03efxn362","country_code":"MX","type":"education","lineage":["https://openalex.org/I147280213"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Acosta-Portilla, Juan Rafael","raw_affiliation_strings":["Instituto de Investigaciones y Estudios Superiores Econ\u00f3micos y Sociales , Universidad Veracruzana , M\u00e9xico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Investigaciones y Estudios Superiores Econ\u00f3micos y Sociales , Universidad Veracruzana , M\u00e9xico","institution_ids":["https://openalex.org/I147280213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030143533"],"corresponding_institution_ids":["https://openalex.org/I147280213"],"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9556000232696533,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9556000232696533,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.010700000450015068,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.005200000014156103,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/equivalent-norms","display_name":"equivalent norms","score":0.7730000019073486},{"id":"https://openalex.org/keywords/minkowski-functionals","display_name":"Minkowski functionals","score":0.7919999957084656},{"id":"https://openalex.org/keywords/simplicial-fans","display_name":"simplicial fans","score":0.9599999785423279},{"id":"https://openalex.org/keywords/polyhedral-norms","display_name":"polyhedral norms","score":0.7289999723434448},{"id":"https://openalex.org/keywords/finite-dimensional-banach-spaces","display_name":"finite-dimensional Banach spaces","score":0.7720000147819519}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8496999740600586},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.5019000172615051},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46790000796318054},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4489000141620636},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.43639999628067017},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.38510000705718994},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3610000014305115},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.34599998593330383},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.33250001072883606},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.32580000162124634},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.3240000009536743},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.31290000677108765},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3107999861240387},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30550000071525574},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.2953000068664551},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28700000047683716},{"id":"https://openalex.org/C158158286","wikidata":"https://www.wikidata.org/wiki/Q9009080","display_name":"Invariants of tensors","level":3,"score":0.27900001406669617},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.27649998664855957},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C12773090","wikidata":"https://www.wikidata.org/wiki/Q3888851","display_name":"Ambient space","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.2581999897956848}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.14035","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14035","pdf_url":"https://arxiv.org/pdf/2609.14035","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.2609.14035","doi":"https://doi.org/10.48550/arxiv.2609.14035","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.14035","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:2609.14035","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14035","pdf_url":"https://arxiv.org/pdf/2609.14035","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/W7213245246.pdf","grobid_xml":"https://content.openalex.org/works/W7213245246.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W587075566","https://openalex.org/W1567142770","https://openalex.org/W1577514385","https://openalex.org/W2082042541","https://openalex.org/W4292754934"],"related_works":["https://openalex.org/W2970805471","https://openalex.org/W2971416451","https://openalex.org/W2896496348","https://openalex.org/W7214303929","https://openalex.org/W2001616683","https://openalex.org/W2079899260","https://openalex.org/W2258459448","https://openalex.org/W7214366063","https://openalex.org/W2024025224","https://openalex.org/W4398150347"],"abstract_inverted_index":{"We":[0,54,81],"study":[1],"finite":[2,27,77,175],"polyhedral":[3,101,183],"models":[4,118,139,176],"inside":[5],"the":[6,21,34,49,56,75,94,99,112,137,143,147,159,164,186],"projectivized":[7],"space":[8,17],"of":[9,36,42,74,189],"equivalent":[10],"norms":[11,102],"$\\mathcal{N}'(X)$":[12],"on":[13,48,97,151,163],"a":[14,26,71,106],"finite-dimensional":[15,182],"Banach":[16],"$X$,":[18],"endowed":[19],"with":[20],"logarithmic":[22,148],"distortion":[23,149],"metric.":[24],"Given":[25],"symmetric":[28,43],"direction":[29,78],"set":[30],"$E$,":[31],"we":[32,110,169],"introduce":[33],"class":[35],"$\u03b1E$-norms,":[37],"defined":[38],"as":[39,129],"Minkowski":[40],"functionals":[41],"polytopes":[44],"whose":[45],"vertices":[46],"lie":[47],"rays":[50],"prescribed":[51],"by":[52,86,133,158],"$E$.":[53],"identify":[55],"admissible":[57,165],"weights":[58],"$\u03b1$":[59],"for":[60,173],"which":[61,92,98],"this":[62,84],"parametrization":[63,73],"is":[64,155],"non-redundant":[65],"and":[66,115,120,122,153,177],"prove":[67,170],"that":[68,124],"they":[69,125,180],"give":[70],"one-to-one":[72],"corresponding":[76,113,144],"model":[79],"$\\mathcal{N}(E)$.":[80],"then":[82],"refine":[83],"description":[85],"introducing":[87],"complete,":[88],"symmetric,":[89],"simplicial":[90],"$E$-fans,":[91],"encode":[93],"conical":[95],"regions":[96],"associated":[100],"are":[103,126],"linear.":[104],"For":[105],"fixed":[107],"fan":[108,117],"$\\mathcal{F}$,":[109],"define":[111],"geometric":[114],"coordinate":[116,138],"$\\mathcal{N}(\\mathcal{F})$":[119],"$\\mathcal{R}(\\mathcal{F})$,":[121],"show":[123,178],"naturally":[127],"isomorphic":[128],"cones.":[130],"After":[131],"quotienting":[132],"positive":[134],"scalar":[135],"multiplication,":[136],"become":[140],"isometric":[141],"to":[142,185],"norm":[145],"models:":[146],"metric":[150,162,187],"$\\mathcal{N}'(E)$":[152],"$\\mathcal{N}'(\\mathcal{F})$":[154],"represented":[156],"exactly":[157],"Hilbert":[160],"projective":[161],"weight":[166],"spaces.":[167],"Finally,":[168],"completeness":[171],"results":[172],"these":[174],"how":[179],"provide":[181],"approximations":[184],"geometry":[188],"$\\mathcal{N}'(X)$.":[190]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}
