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Germs of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products
-
Ngaiming Mok
and
Sui Chung Ng
Published/Copyright:
September 26, 2011
Abstract
Let 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.
Received: 2009-12-29
Revised: 2011-01-05
Published Online: 2011-09-26
Published in Print: 2012-08
©[2012] by Walter de Gruyter Berlin Boston
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- String topology of classifying spaces
- Germs of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products
- Weak Neumann implies Stokes
- Quasi-isometric classification of non-geometric 3-manifold groups
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Articles in the same Issue
- String topology of classifying spaces
- Germs of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products
- Weak Neumann implies Stokes
- Quasi-isometric classification of non-geometric 3-manifold groups
- Thomae type formula for K3 surfaces given by double covers of the projective plane branching along six lines
- Cosmetic crossing changes of fibered knots
- Leavitt path algebras of separated graphs
- Brauer's height zero conjecture for the 2-blocks of maximal defect
