{"id":"https://openalex.org/W2054535895","doi":"https://doi.org/10.1145/1377676.1377686","title":"Markov convexity and local rigidity of distorted metrics","display_name":"Markov convexity and local rigidity of distorted metrics","publication_year":2008,"publication_date":"2008-06-09","ids":{"openalex":"https://openalex.org/W2054535895","doi":"https://doi.org/10.1145/1377676.1377686","mag":"2054535895"},"language":"en","primary_location":{"id":"doi:10.1145/1377676.1377686","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1377676.1377686","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-fourth annual symposium on Computational geometry","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://ems.press/content/serial-article-files/5380","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014833431","display_name":"Manor Mendel","orcid":"https://orcid.org/0000-0002-7521-0358"},"institutions":[{"id":"https://openalex.org/I164950643","display_name":"Open University of Israel","ror":"https://ror.org/027z64205","country_code":"IL","type":"education","lineage":["https://openalex.org/I164950643"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Manor Mendel","raw_affiliation_strings":["The Open University of Israel, Raanana, Israel","Open University of Israel"],"affiliations":[{"raw_affiliation_string":"The Open University of Israel, Raanana, Israel","institution_ids":["https://openalex.org/I164950643"]},{"raw_affiliation_string":"Open University of Israel","institution_ids":["https://openalex.org/I164950643"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052985577","display_name":"Assaf Naor","orcid":null},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Assaf Naor","raw_affiliation_strings":["New York University, United States","New York University"],"affiliations":[{"raw_affiliation_string":"New York University, United States","institution_ids":[]},{"raw_affiliation_string":"New York University","institution_ids":["https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014833431"],"corresponding_institution_ids":["https://openalex.org/I164950643"],"apc_list":null,"apc_paid":null,"fwci":0.86,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.69820854,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"15","issue":"1","first_page":"287","last_page":"337"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9988999962806702,"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":0.9988999962806702,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9969000220298767,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9955000281333923,"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/convexity","display_name":"Convexity","score":0.8698766231536865},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7394141554832458},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.6790637969970703},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5774762630462646},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.572167694568634},{"id":"https://openalex.org/keywords/uniformly-convex-space","display_name":"Uniformly convex space","score":0.559623122215271},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5548214316368103},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5063213109970093},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.49285173416137695},{"id":"https://openalex.org/keywords/rigidity","display_name":"Rigidity (electromagnetism)","score":0.47029563784599304},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.4560754597187042},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3881445825099945},{"id":"https://openalex.org/keywords/lp-space","display_name":"Lp space","score":0.17410728335380554},{"id":"https://openalex.org/keywords/banach-manifold","display_name":"Banach manifold","score":0.12866830825805664},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07661992311477661},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06392845511436462}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8698766231536865},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7394141554832458},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6790637969970703},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5774762630462646},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.572167694568634},{"id":"https://openalex.org/C123413131","wikidata":"https://www.wikidata.org/wiki/Q847535","display_name":"Uniformly convex space","level":5,"score":0.559623122215271},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5548214316368103},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5063213109970093},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.49285173416137695},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.47029563784599304},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4560754597187042},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3881445825099945},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.17410728335380554},{"id":"https://openalex.org/C165593952","wikidata":"https://www.wikidata.org/wiki/Q3554819","display_name":"Banach manifold","level":4,"score":0.12866830825805664},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07661992311477661},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06392845511436462},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","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},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1377676.1377686","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1377676.1377686","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-fourth annual symposium on Computational geometry","raw_type":"proceedings-article"},{"id":"doi:10.4171/jems/362","is_oa":true,"landing_page_url":"https://doi.org/10.4171/jems/362","pdf_url":"https://ems.press/content/serial-article-files/5380","source":{"id":"https://openalex.org/S88235189","display_name":"Journal of the European Mathematical Society","issn_l":"1435-9855","issn":["1435-9855","1435-9863"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310316982","host_organization_name":"European Mathematical Society","host_organization_lineage":["https://openalex.org/P4310316982"],"host_organization_lineage_names":["European Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the European Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0803.1697","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0803.1697","pdf_url":"https://arxiv.org/pdf/0803.1697","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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.0803.1697","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0803.1697","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article-journal"}],"best_oa_location":{"id":"doi:10.4171/jems/362","is_oa":true,"landing_page_url":"https://doi.org/10.4171/jems/362","pdf_url":"https://ems.press/content/serial-article-files/5380","source":{"id":"https://openalex.org/S88235189","display_name":"Journal of the European Mathematical Society","issn_l":"1435-9855","issn":["1435-9855","1435-9863"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310316982","host_organization_name":"European Mathematical Society","host_organization_lineage":["https://openalex.org/P4310316982"],"host_organization_lineage_names":["European Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the European Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6095639990","display_name":null,"funder_award_id":"221/07","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G6752600216","display_name":null,"funder_award_id":"0832795","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8096650857","display_name":"Efficient algorithms and data structures via geometric realizations","funder_award_id":"0635078","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"},{"id":"https://openalex.org/F4320306079","display_name":"David and Lucile Packard Foundation","ror":"https://ror.org/032atxq54"},{"id":"https://openalex.org/F4320307791","display_name":"Cisco Systems","ror":"https://ror.org/03yt1ez60"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2054535895.pdf","grobid_xml":"https://content.openalex.org/works/W2054535895.grobid-xml"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W4516790","https://openalex.org/W76622595","https://openalex.org/W148397604","https://openalex.org/W209159601","https://openalex.org/W1483679902","https://openalex.org/W1499647122","https://openalex.org/W1523918473","https://openalex.org/W1594954118","https://openalex.org/W1602756358","https://openalex.org/W1603375414","https://openalex.org/W1845187874","https://openalex.org/W1857462304","https://openalex.org/W1963961606","https://openalex.org/W1968333148","https://openalex.org/W1981853164","https://openalex.org/W1989718296","https://openalex.org/W1991407886","https://openalex.org/W1997263634","https://openalex.org/W1997307133","https://openalex.org/W2001075173","https://openalex.org/W2007810353","https://openalex.org/W2010418491","https://openalex.org/W2010832227","https://openalex.org/W2017571334","https://openalex.org/W2018828794","https://openalex.org/W2020307187","https://openalex.org/W2035259373","https://openalex.org/W2036959865","https://openalex.org/W2043174865","https://openalex.org/W2047213100","https://openalex.org/W2049388783","https://openalex.org/W2055731028","https://openalex.org/W2060691299","https://openalex.org/W2065195508","https://openalex.org/W2066864620","https://openalex.org/W2076459508","https://openalex.org/W2079461683","https://openalex.org/W2082287043","https://openalex.org/W2085984521","https://openalex.org/W2088589971","https://openalex.org/W2097636047","https://openalex.org/W2105160468","https://openalex.org/W2151592438","https://openalex.org/W2295300543","https://openalex.org/W2610052675","https://openalex.org/W2950422632","https://openalex.org/W2951934552","https://openalex.org/W2962980142","https://openalex.org/W2963503996","https://openalex.org/W2964116518","https://openalex.org/W3037473696","https://openalex.org/W3126138554","https://openalex.org/W4232813473","https://openalex.org/W6600197706","https://openalex.org/W6603093367","https://openalex.org/W6631282669","https://openalex.org/W6662609768"],"related_works":["https://openalex.org/W3100090542","https://openalex.org/W2110382157","https://openalex.org/W2088589971","https://openalex.org/W2120860655","https://openalex.org/W2963596328","https://openalex.org/W1996126957","https://openalex.org/W2053983883","https://openalex.org/W2001904056","https://openalex.org/W3099055239","https://openalex.org/W2085984521","https://openalex.org/W3106489028","https://openalex.org/W2085640574","https://openalex.org/W2166790036","https://openalex.org/W2138687936","https://openalex.org/W1973828847","https://openalex.org/W2130644855","https://openalex.org/W2085880780","https://openalex.org/W2964296314","https://openalex.org/W2018828794"],"abstract_inverted_index":{"It":[0],"is":[1,24],"shown":[2],"that":[3,45],"a":[4],"Banach":[5],"space":[6],"admits":[7],"an":[8],"equivalent":[9],"norm":[10],"whose":[11],"modulus":[12],"of":[13,39],"uniform":[14,37],"convexity":[15,38],"has":[16],"power-type":[17],"p":[18,26],"if":[19,22],"and":[20],"only":[21],"it":[23],"Markov":[25],"-convex.":[27],"Counterexamples":[28],"are":[29],"constructed":[30],"to":[31,35,49],"natural":[32],"questions":[33],"related":[34],"isomorphic":[36],"metric":[40],"spaces,":[41],"showing":[42],"in":[43],"particular":[44],"tree":[46],"metrics":[47],"fail":[48],"have":[50],"the":[51],"dichotomy":[52],"property.":[53]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2016-06-24T00:00:00"}