{"id":"https://openalex.org/W2079661591","doi":"https://doi.org/10.1155/ijmms/2006/23656","title":"Horoballs in simplices and Minkowski spaces","display_name":"Horoballs in simplices and Minkowski spaces","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2079661591","doi":"https://doi.org/10.1155/ijmms/2006/23656","mag":"2079661591"},"language":"en","primary_location":{"id":"doi:10.1155/ijmms/2006/23656","is_oa":true,"landing_page_url":"https://doi.org/10.1155/ijmms/2006/23656","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2006/023656.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2006/023656.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101680741","display_name":"Anders Karlsson","orcid":"https://orcid.org/0000-0002-1886-6780"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"A. Karlsson","raw_affiliation_strings":["Department of Mathematics, Royal Institute of Technology, Stockholm 10044"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Royal Institute of Technology, Stockholm 10044","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029581609","display_name":"Volker Metz","orcid":"https://orcid.org/0000-0001-8858-6218"},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"V. Metz","raw_affiliation_strings":["Faculty of Mathematics, Bielefeld University, Bielefeld 33501"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Bielefeld University, Bielefeld 33501","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022859235","display_name":"\u0413. \u0410. \u041d\u043e\u0441\u043a\u043e\u0432","orcid":"https://orcid.org/0000-0003-3314-0942"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"G. A. Noskov","raw_affiliation_strings":["Sobolev Institute of Mathematics, Pevtsova 13, Omsk 644099"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics, Pevtsova 13, Omsk 644099","institution_ids":["https://openalex.org/I4210096862"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":4.9421,"has_fulltext":true,"cited_by_count":39,"citation_normalized_percentile":{"value":0.95571917,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2006","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9972000122070312,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9969000220298767,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/mathematics","display_name":"Mathematics","score":0.873802900314331},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.7968935966491699},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.6938197016716003},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6211437582969666},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5395722389221191},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5207464694976807},{"id":"https://openalex.org/keywords/locally-convex-topological-vector-space","display_name":"Locally convex topological vector space","score":0.5173620581626892},{"id":"https://openalex.org/keywords/normed-vector-space","display_name":"Normed vector space","score":0.5157271027565002},{"id":"https://openalex.org/keywords/convex-geometry","display_name":"Convex geometry","score":0.5107455253601074},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.49261027574539185},{"id":"https://openalex.org/keywords/minkowski-addition","display_name":"Minkowski addition","score":0.4324198365211487},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.28869539499282837},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.27924996614456177},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.0939173698425293}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.873802900314331},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.7968935966491699},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.6938197016716003},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6211437582969666},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5395722389221191},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5207464694976807},{"id":"https://openalex.org/C58228006","wikidata":"https://www.wikidata.org/wiki/Q1572357","display_name":"Locally convex topological vector space","level":3,"score":0.5173620581626892},{"id":"https://openalex.org/C171739935","wikidata":"https://www.wikidata.org/wiki/Q726210","display_name":"Normed vector space","level":2,"score":0.5157271027565002},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.5107455253601074},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.49261027574539185},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.4324198365211487},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28869539499282837},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.27924996614456177},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.0939173698425293},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/ijmms/2006/23656","is_oa":true,"landing_page_url":"https://doi.org/10.1155/ijmms/2006/23656","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2006/023656.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:023656","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2006/023656.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:64fa2b9550af4d86ba7648fd55945766","is_oa":false,"landing_page_url":"https://doaj.org/article/64fa2b9550af4d86ba7648fd55945766","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2006 (2006)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/ijmms/2006/23656","is_oa":true,"landing_page_url":"https://doi.org/10.1155/ijmms/2006/23656","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2006/023656.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"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/W2079661591.pdf","grobid_xml":"https://content.openalex.org/works/W2079661591.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W59035359","https://openalex.org/W1553702074","https://openalex.org/W1559761527","https://openalex.org/W1598917891","https://openalex.org/W1972401387","https://openalex.org/W1992864421","https://openalex.org/W2014307924","https://openalex.org/W2016358031","https://openalex.org/W2042645706","https://openalex.org/W2055412056","https://openalex.org/W2058415421","https://openalex.org/W2087469306","https://openalex.org/W2112861192","https://openalex.org/W2134309556","https://openalex.org/W2945305319","https://openalex.org/W2963857408","https://openalex.org/W3098362445","https://openalex.org/W3159824982","https://openalex.org/W4213195349","https://openalex.org/W4244635799","https://openalex.org/W6929881615"],"related_works":["https://openalex.org/W103014951","https://openalex.org/W2486282296","https://openalex.org/W4250479592","https://openalex.org/W1992584347","https://openalex.org/W3121434904","https://openalex.org/W1577220984","https://openalex.org/W4231121233","https://openalex.org/W4236145557","https://openalex.org/W2272980419","https://openalex.org/W4245268118"],"abstract_inverted_index":{"We":[0],"obtain":[1],"precise":[2],"descriptions":[3],"of":[4,40,43,46],"all":[5],"horoballs":[6],"for":[7,13],"Hilbert\u2032s":[8],"geometry":[9],"on":[10],"simplices":[11],"and":[12,29],"normed":[14],"finite\u2010dimensional":[15],"vector":[16],"spaces":[17],"with":[18],"norm":[19],"given":[20],"by":[21],"some":[22],"polyhedron.":[23],"Certain":[24],"geometrical":[25],"consequences":[26],"are":[27,33],"deduced":[28],"several":[30],"other":[31],"applications":[32],"pointed":[34],"out,":[35],"which":[36],"concern":[37],"the":[38],"dynamics":[39],"important":[41],"classes":[42],"nonlinear":[44],"self\u2010maps":[45],"convex":[47],"cones.":[48]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}