{"id":"https://openalex.org/W2086909375","doi":"https://doi.org/10.1090/s0002-9947-1981-0597876-7","title":"Quasi-Symmetric Embeddings in Euclidean Spaces","display_name":"Quasi-Symmetric Embeddings in Euclidean Spaces","publication_year":1981,"publication_date":"1981-01-01","ids":{"openalex":"https://openalex.org/W2086909375","doi":"https://doi.org/10.1090/s0002-9947-1981-0597876-7","mag":"2086909375"},"language":"en","primary_location":{"id":"doi:10.1090/s0002-9947-1981-0597876-7","doi":"https://doi.org/10.1090/s0002-9947-1981-0597876-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1981-0597876-7","pdf_url":"https://www.ams.org/tran/1981-264-01/S0002-9947-1981-0597876-7/S0002-9947-1981-0597876-7.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/tran/1981-264-01/S0002-9947-1981-0597876-7/S0002-9947-1981-0597876-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044168966","display_name":"Jussi V\u00e4\u0131s\u00e4l\u00e4","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jussi V\u00e4is\u00e4l\u00e4","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5044168966"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7945,"has_fulltext":true,"cited_by_count":107,"citation_normalized_percentile":{"value":0.94170945,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":97},"biblio":{"volume":"264","issue":"1","first_page":"191","last_page":"191"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.43869999051094055,"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/T11822","display_name":"Analytic and geometric function theory","score":0.43869999051094055,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.18369999527931213,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.155799999833107,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quasiconformal-mappings","display_name":"quasiconformal mappings","score":0.925000011920929},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.925000011920929},{"id":"https://openalex.org/keywords/hausdorff-measure","display_name":"Hausdorff measure","score":0.9649999737739563},{"id":"https://openalex.org/keywords/open-subsets-of-euclidean-space","display_name":"open subsets of Euclidean space","score":0.6700000166893005}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6385113000869751},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.43869760632514954},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.43630844354629517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42634934186935425}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0002-9947-1981-0597876-7","doi":"https://doi.org/10.1090/s0002-9947-1981-0597876-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1981-0597876-7","pdf_url":"https://www.ams.org/tran/1981-264-01/S0002-9947-1981-0597876-7/S0002-9947-1981-0597876-7.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},{"id":"doi:10.2307/1998419","doi":"https://doi.org/10.2307/1998419","is_oa":false,"landing_page_url":"https://doi.org/10.2307/1998419","pdf_url":null,"source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0002-9947-1981-0597876-7","doi":"https://doi.org/10.1090/s0002-9947-1981-0597876-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1981-0597876-7","pdf_url":"https://www.ams.org/tran/1981-264-01/S0002-9947-1981-0597876-7/S0002-9947-1981-0597876-7.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2086909375.pdf","grobid_xml":"https://content.openalex.org/works/W2086909375.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W130551811","https://openalex.org/W1516308076","https://openalex.org/W1519970706","https://openalex.org/W1522020530","https://openalex.org/W1553738528","https://openalex.org/W1978934719","https://openalex.org/W2032925799","https://openalex.org/W2052563939","https://openalex.org/W2138819861","https://openalex.org/W2314109566","https://openalex.org/W2318895797"],"related_works":["https://openalex.org/W15886813","https://openalex.org/W2607536060","https://openalex.org/W7203441652","https://openalex.org/W196548951","https://openalex.org/W70345882","https://openalex.org/W2032925799","https://openalex.org/W2314259074","https://openalex.org/W1485219104","https://openalex.org/W2318278878","https://openalex.org/W7098431642"],"abstract_inverted_index":{"We":[0,123],"consider":[1],"quasi-symmetric":[2,115],"embeddings":[3],"f":[4,64,74,83,84],":":[5],"G":[6,14,15,45,46,65,75],"\u2192":[7],"R":[8,18,110],"n":[9,24,27,32,35,55,58,70,71,98,101,103,106,111],"f:G":[10],"\\to":[11],"{R^n}":[12,112],",":[13,21,36,59,109],"open":[16],"in":[17],"p":[19,22,25,30,33,53,56,80,81,91,92,96,99,116,117],"{R^p}":[20],"\u2a7d":[23],"\\leqslant":[26],".":[28,72],"If":[29,52,73,95],"=":[31,34],"quasi-symmetry":[37],"implies":[38],"quasi-conformality.":[39],"The":[40],"converse":[41],"is":[42,67,120],"true":[43],"if":[44],"has":[47,77],"a":[48,78,114],"sufficiently":[49],"smooth":[50],"boundary.":[51],">":[54,57,97,100],"the":[60,86,129],"Hausdorff":[61,132],"dimension":[62],"of":[63,88,90],"fG":[66,76],"less":[68],"than":[69],"finite":[79],"-measure,":[82],"preserves":[85],"property":[87],"being":[89],"-measure":[93],"zero.":[94],"and":[102,134],"\u2a7e":[104],"3":[105,108],"\\geqslant":[107],"contains":[113],"-cell":[118],"which":[119],"topologically":[121],"wild.":[122],"also":[124],"prove":[125],"auxiliary":[126],"results":[127],"on":[128],"relations":[130],"between":[131],"measure":[133],"\u010cech":[135],"cohomology.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2016-06-24T00:00:00"}