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Article: Germs of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products

TitleGerms of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products
Authors
Issue Date2012
PublisherWalter de Gruyter GmbH & Co KG. The Journal's web site is located at http://www.degruyter.com/view/j/crll?rskey=R7TouQ&result=189&q=
Citation
Journal für die Reine und Angewandte Mathematik, 2012, n. 669, p. 47-73 How to Cite?
AbstractLet X be the quotient of an irreducible bounded symmetric domain Ω by a lattice. In order to characterize algebraic correspondences on X commuting with exterior Hecke correspondences, Clozel–Ullmo studied certain germs of measure-preserving maps from (Ω; 0) into its Cartesian products, proving that such maps are totally geodesic when dim(X) = 1. Here we prove total geodesy when dim(Ω) ≧ 2 by methods of analytic continuation. For Bn, n ≧ 2, total geodesy follows then from Alexander's theorem. When rank(Ω) ≧ 2, we deduce total geodesy from Alexander-type theorems, especially from a new Alexander-type theorem involving Reg(∂Ω) in place of the Shilov boundary.
Persistent Identifierhttp://hdl.handle.net/10722/152702
ISSN
2019 Impact Factor: 1.486
2015 SCImago Journal Rankings: 3.614
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorMok, N-
dc.contributor.authorNg, SC-
dc.date.accessioned2012-07-16T09:46:37Z-
dc.date.available2012-07-16T09:46:37Z-
dc.date.issued2012-
dc.identifier.citationJournal für die Reine und Angewandte Mathematik, 2012, n. 669, p. 47-73-
dc.identifier.issn0075-4102-
dc.identifier.urihttp://hdl.handle.net/10722/152702-
dc.description.abstractLet X be the quotient of an irreducible bounded symmetric domain Ω by a lattice. In order to characterize algebraic correspondences on X commuting with exterior Hecke correspondences, Clozel–Ullmo studied certain germs of measure-preserving maps from (Ω; 0) into its Cartesian products, proving that such maps are totally geodesic when dim(X) = 1. Here we prove total geodesy when dim(Ω) ≧ 2 by methods of analytic continuation. For Bn, n ≧ 2, total geodesy follows then from Alexander's theorem. When rank(Ω) ≧ 2, we deduce total geodesy from Alexander-type theorems, especially from a new Alexander-type theorem involving Reg(∂Ω) in place of the Shilov boundary.-
dc.languageeng-
dc.publisherWalter de Gruyter GmbH & Co KG. The Journal's web site is located at http://www.degruyter.com/view/j/crll?rskey=R7TouQ&result=189&q=-
dc.relation.ispartofJournal für die Reine und Angewandte Mathematik-
dc.rights© Walter de Gruyter Berlin · Boston 2012. The final publication is available at www.degruyter.com-
dc.titleGerms of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products-
dc.typeArticle-
dc.identifier.emailMok, N: nmok@hku.hk-
dc.identifier.emailNg, SC: h0008312@hkusua.hku.hk-
dc.identifier.authorityMok, N=rp00763-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1515/CRELLE.2011.142-
dc.identifier.scopuseid_2-s2.0-84870219948-
dc.identifier.hkuros201003-
dc.identifier.issue669-
dc.identifier.spage47-
dc.identifier.epage73-
dc.identifier.isiWOS:000309042900002-
dc.publisher.placeGermany-

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