{"id":"https://openalex.org/W1964353233","doi":"https://doi.org/10.1007/s00209-006-0041-z","title":"On chordal and bilateral SLE in multiply connected domains","display_name":"On chordal and bilateral SLE in multiply connected domains","publication_year":2007,"publication_date":"2007-11-05","ids":{"openalex":"https://openalex.org/W1964353233","doi":"https://doi.org/10.1007/s00209-006-0041-z","mag":"1964353233"},"language":"en","primary_location":{"id":"doi:10.1007/s00209-006-0041-z","doi":"https://doi.org/10.1007/s00209-006-0041-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00209-006-0041-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00209-006-0041-z.pdf","source":{"id":"https://openalex.org/S104894821","display_name":"Mathematische Zeitschrift","issn_l":"0025-5874","issn":["0025-5874","1432-1823"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-2","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematische Zeitschrift","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00209-006-0041-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113477594","display_name":"Robert Otto Bauer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert O. Bauer","raw_affiliation_strings":["Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL, 61801, USA","University of Illinois at Urbana Champaign"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL, 61801, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"University of Illinois at Urbana Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109973209","display_name":"R. Friedrich","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Roland M. Friedrich","raw_affiliation_strings":["Max-Planck Institut f\u00fcr Mathematik, 53111, Bonn, Germany","Max\u2014Planck\u2014Institut f\u00fcr Mathematik"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck Institut f\u00fcr Mathematik, 53111, Bonn, Germany","institution_ids":["https://openalex.org/I4210119712"]},{"raw_affiliation_string":"Max\u2014Planck\u2014Institut f\u00fcr Mathematik","institution_ids":["https://openalex.org/I4210119712"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113477594"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":{"value":3290,"currency":"USD","value_usd":3290},"fwci":3.2307,"has_fulltext":true,"cited_by_count":54,"citation_normalized_percentile":{"value":0.90418325,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":98},"biblio":{"volume":"258","issue":"2","first_page":"241","last_page":"265"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9398999810218811,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9398999810218811,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.01899999938905239,"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/T11822","display_name":"Analytic and geometric function theory","score":0.012500000186264515,"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/schramm-loewner-evolution","display_name":"Schramm-Loewner evolution","score":0.906000018119812},{"id":"https://openalex.org/keywords/chordal-sle","display_name":"chordal SLE","score":0.9620000123977661},{"id":"https://openalex.org/keywords/multiply-connected-domains","display_name":"multiply connected domains","score":0.906000018119812},{"id":"https://openalex.org/keywords/conformal-symmetry","display_name":"conformal invariance","score":0.8870000243186951},{"id":"https://openalex.org/keywords/loewner-equation","display_name":"Loewner equation","score":0.8309999704360962},{"id":"https://openalex.org/keywords/boundary-motion","display_name":"boundary motion","score":0.7099999785423279},{"id":"https://openalex.org/keywords/markov-property","display_name":"Markov property","score":0.8870000243186951},{"id":"https://openalex.org/keywords/locality","display_name":"locality","score":0.675000011920929},{"id":"https://openalex.org/keywords/boundary-interactions","display_name":"boundary interactions","score":0.4259999990463257}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8289663791656494},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6195283532142639},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.5382112860679626},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5363079309463501},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5014934539794922},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.45266494154930115},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.42997997999191284},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.41030073165893555},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.22647306323051453},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07428759336471558},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s00209-006-0041-z","doi":"https://doi.org/10.1007/s00209-006-0041-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00209-006-0041-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00209-006-0041-z.pdf","source":{"id":"https://openalex.org/S104894821","display_name":"Mathematische Zeitschrift","issn_l":"0025-5874","issn":["0025-5874","1432-1823"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-2","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematische Zeitschrift","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0503178","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0503178","pdf_url":"https://arxiv.org/pdf/math/0503178","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":"pmh:oai:CiteSeerX.psu:10.1.1.234.4618","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.4618","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0503178v1.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:405355","doi":null,"is_oa":false,"landing_page_url":"http://edoc.mpg.de/405355","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Mathematische Zeitschrift, v.258, 241-265 (2008)","raw_type":"Article"},{"id":"pmh:oai:pure.mpg.de:item_3123746","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/21.11116/0000-0004-291C-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematische Zeitschrift","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.math/0503178","doi":"https://doi.org/10.48550/arxiv.math/0503178","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.math/0503178","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":"doi:10.1007/s00209-006-0041-z","doi":"https://doi.org/10.1007/s00209-006-0041-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00209-006-0041-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00209-006-0041-z.pdf","source":{"id":"https://openalex.org/S104894821","display_name":"Mathematische Zeitschrift","issn_l":"0025-5874","issn":["0025-5874","1432-1823"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-2","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematische Zeitschrift","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322434","display_name":"Max-Planck-Gesellschaft","ror":"https://ror.org/01hhn8329"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1964353233.pdf","grobid_xml":"https://content.openalex.org/works/W1964353233.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W109645894","https://openalex.org/W141124078","https://openalex.org/W1409528260","https://openalex.org/W1495424320","https://openalex.org/W1518739418","https://openalex.org/W1545370368","https://openalex.org/W1572544837","https://openalex.org/W1631898216","https://openalex.org/W1781718690","https://openalex.org/W2000662066","https://openalex.org/W2001412700","https://openalex.org/W2009930506","https://openalex.org/W2010832263","https://openalex.org/W2033077893","https://openalex.org/W2037059152","https://openalex.org/W2037440254","https://openalex.org/W2042379031","https://openalex.org/W2048825720","https://openalex.org/W2050635650","https://openalex.org/W2062541756","https://openalex.org/W2064685239","https://openalex.org/W2112136003","https://openalex.org/W2120645838","https://openalex.org/W2322016700","https://openalex.org/W2328905711","https://openalex.org/W2500638084","https://openalex.org/W2798922842","https://openalex.org/W2949895073","https://openalex.org/W2951944263","https://openalex.org/W3100740946"],"related_works":["https://openalex.org/W2001412700","https://openalex.org/W2923838426","https://openalex.org/W2979344897","https://openalex.org/W3101760604","https://openalex.org/W2122326745","https://openalex.org/W3100565044","https://openalex.org/W1781718690","https://openalex.org/W2895828381","https://openalex.org/W2963591268","https://openalex.org/W7100036614"],"abstract_inverted_index":{"We":[0,30,57,72,181,215],"discuss":[1,170],"the":[2,16,33,36,46,49,69,78,84,95,98,101,106,109,115,120,125,131,138,142,146,150,157,174,184,197,206,209,213,218,222,229],"possible":[3,175,185],"candidates":[4,186],"for":[5,68,225],"conformally":[6,176],"invariant":[7,177],"random":[8,112,122,139,147,178,210,219],"non-self-crossing":[9,179],"curves":[10,113],"which":[11,25,204],"begin":[12],"and":[13,24,45,86,103,169],"end":[14],"on":[15,83,124,141],"boundary":[17,40,54,85,126,143],"of":[18,61,97,100,149,194,200,208,228],"a":[19,27,39,75,81,153],"multiply":[20,65,134],"connected":[21,66],"planar":[22],"domain,":[23],"satisfy":[26],"Markovian-type":[28],"property.":[29],"consider":[31],"both,":[32],"case":[34,47],"when":[35,48],"curve":[37,50,76,107,211,220],"connects":[38,51],"component":[41],"to":[42,64,92],"itself":[43],"(chordal),":[44],"two":[52,70,190],"different":[53],"components":[55],"(bilateral).":[56],"establish":[58],"appropriate":[59,226],"extensions":[60],"Loewner\u2019s":[62],"equation":[63],"domains":[67],"cases.":[71],"show":[73,118,161,182,216],"that":[74,87,119,137,162,183,217],"in":[77,108,114],"domain":[79,102,132],"induces":[80],"motion":[82,89,96,123,140,148],"this":[88,163,172],"is":[90,127,133],"enough":[91],"first":[93],"recover":[94],"moduli":[99,151],"then,":[104],"second,":[105],"interior.":[110],"For":[111],"interior":[116],"we":[117,160],"induced":[121],"not":[128],"Markov":[129,154,164],"if":[130],"connected,":[135],"but":[136],"together":[144],"with":[145,212],"forms":[152],"process.":[155],"In":[156],"chordal":[158],"case,":[159],"process":[165],"satisfies":[166],"Brownian":[167],"scaling":[168],"how":[171],"limits":[173],"curves.":[180],"are":[187],"labeled":[188],"by":[189],"functions,":[191],"one":[192],"homogeneous":[193,199],"degree":[195,201],"zero,":[196],"other":[198],"minus":[202],"one,":[203],"describes":[205],"interaction":[207,230],"boundary.":[214],"has":[221],"locality":[223],"property":[224],"choices":[227],"term.":[231]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}