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Licensed Unlicensed Requires Authentication Published by De Gruyter September 26, 2011

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

Ngaiming Mok and Sui Chung Ng

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