Germs of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products
Germs of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products
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DOI：
10.1515/crelle.2011.142
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
N. Mok;Sui-Chung Ng
中科院分区：
文献类型：
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作者：
N. Mok;Sui-Chung Ng
摘要 设 X 为不可约有界对称域 Ω 与格的商。为了表征 X 上与外部 Hecke 对应关系的代数对应关系，Clozel-Ullmo 研究了从 (Ω; 0) 到其笛卡尔积的保测映射的某些萌芽，证明了当 dim(X) = 1 时这些映射是完全测地线的。这里我们通过解析延拓的方法证明了当 dim(Ω) ≧ 2 时的全测地线。对于 Bn，n ≧ 2，则总大地测量可从亚历山大定理得出。当rank(Ω) ≧ 2时，我们从Alexander型定理推导出总测地学，特别是从涉及Reg(∂Ω)代替Shilov边界的新Alexander型定理推导出来。
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.