{"id":"https://openalex.org/W4367190850","doi":"https://doi.org/10.48550/arxiv.2304.13600","title":"Valuations in affine convex geometry","display_name":"Valuations in affine convex geometry","publication_year":2023,"publication_date":"2023-04-26","ids":{"openalex":"https://openalex.org/W4367190850","doi":"https://doi.org/10.48550/arxiv.2304.13600"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2304.13600","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2304.13600","pdf_url":"https://arxiv.org/pdf/2304.13600","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/2304.13600","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089582758","display_name":"Jakob Henkel","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Henkel, Jakob","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5086811650","display_name":"Thomas Wannerer","orcid":"https://orcid.org/0000-0003-2533-8430","observed_orcids":["https://orcid.org/0000-0003-2533-8430"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wannerer, Thomas","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/T11830","display_name":"Point processes and geometric inequalities","score":0.9990000128746033,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9990000128746033,"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":0.0005000000237487257,"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"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/valuation","display_name":"valuation","score":0.7400000095367432},{"id":"https://openalex.org/keywords/convex-bodies","display_name":"convex bodies","score":0.9549999833106995},{"id":"https://openalex.org/keywords/projection-bodies","display_name":"projection bodies","score":0.9950000047683716},{"id":"https://openalex.org/keywords/volume","display_name":"volume","score":0.5260000228881836},{"id":"https://openalex.org/keywords/translation-invariance","display_name":"translation invariance","score":0.7799999713897705},{"id":"https://openalex.org/keywords/continuous-valuations","display_name":"continuous valuations","score":0.6679999828338623}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7186856269836426},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6815885305404663},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.6142125129699707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.507904589176178},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.44670048356056213},{"id":"https://openalex.org/C23684344","wikidata":"https://www.wikidata.org/wiki/Q382520","display_name":"Affine geometry","level":4,"score":0.4166387915611267},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36428117752075195},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3561292886734009},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3486975431442261},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.21711289882659912},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.16642889380455017}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2304.13600","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2304.13600","pdf_url":"https://arxiv.org/pdf/2304.13600","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.2304.13600","doi":"https://doi.org/10.48550/arxiv.2304.13600","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2304.13600","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2304.13600","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2304.13600","pdf_url":"https://arxiv.org/pdf/2304.13600","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G748164020","display_name":null,"funder_award_id":"WA 3510/3-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4367190850.pdf","grobid_xml":"https://content.openalex.org/works/W4367190850.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4287823846","https://openalex.org/W3013271942","https://openalex.org/W1667131232","https://openalex.org/W2131092941","https://openalex.org/W2037443895","https://openalex.org/W1491504611","https://openalex.org/W1601587252","https://openalex.org/W2038416447","https://openalex.org/W1976822125","https://openalex.org/W1988671459"],"abstract_inverted_index":{"In":[0,53],"convex":[1,9,40],"geometry,":[2],"the":[3,19,38,49,58],"constructions":[4,64],"that":[5],"assign":[6],"to":[7],"a":[8,70,84],"body":[10],"its":[11],"difference":[12],"body,":[13,15],"projection":[14],"or":[16],"volume":[17],"have":[18],"following":[20],"properties:":[21],"They":[22],"are":[23,42,74],"(1)":[24],"invariant":[25],"under":[26],"volume-preserving":[27],"linear":[28,51],"changes":[29],"of":[30,44,48,86],"coordinates;":[31],"(2)":[32],"continuous;":[33],"(3)":[34],"finitely":[35],"additive,":[36],"and":[37],"resulting":[39],"bodies":[41],"subsets":[43],"an":[45],"irreducible":[46],"representation":[47],"special":[50],"group.":[52],"this":[54,89],"paper":[55],"we":[56],"explore":[57],"question":[59],"whether":[60],"there":[61],"exist":[62],"other":[63],"with":[65],"these":[66],"properties.":[67],"We":[68],"discover":[69],"surprising":[71],"dichotomy:":[72],"There":[73],"no":[75],"new":[76],"examples":[77,87],"if":[78],"one":[79],"assumes":[80],"translation":[81],"invariance,":[82],"but":[83],"plethora":[85],"without":[88],"assumption.":[90]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}