Tilings and finite energy retractions of locally symmetric spaces
Tilings and finite energy retractions of locally symmetric spaces
复制标题
局部对称空间的平铺和有限能量回缩
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
Leslie Saper
中科院分区：
文献类型：
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作者：
Leslie Saper
抽象。让
$伽玛 {X} $是算术商的Borel-Serre紧集
$伽玛 一个非紧型对称空间的空间。我们建造天然的瓷砖
$伽玛 ackslash overline{X} = coprod _P Gamma ackslash覆盖{X}_P $（取决于参数B），其推广了
$伽玛 我是X $。这是适用于产生一个自然的分段分析变形收缩，
$伽玛 将{X} $上划线到带角的紧致子流形上
$伽玛 ackslash X _0子集Gamma 我是X $。事实上，我们证明了
$伽玛 ackslash X _0 $是（在自然分段解析同态下）
$伽玛 内部的ackslash上划线{X} $
$伽玛 我是X $。为了应用于调和映射和几何刚性理论，我们证明了除了少数低秩的例子外，这种收缩和复同态具有有限的能量。我们还使用平铺给出了一个明确的描述，一个共尾家庭的邻里面，
$伽玛 ackslash overline{X} $，并研究了镶嵌对参数B的依赖性以及镶嵌的退化。
Abstract. Let
$ Gamma ackslash overline{X} $ be the Borel-Serre compactifiction of an arithmetic quotient
$ Gamma ackslash X $ of a symmetric space of noncompact type. We construct natural tilings
$ Gamma ackslash overline{X} = coprod _P Gamma ackslash overline{X}_P $ (depending on a parameter b) which generalize the Arthur-Langlands partition of
$ Gamma ackslash X $. This is applied to yield a natural piecewise analytic deformation retraction of
$ Gamma ackslash overline{X} $ onto a compact submanifold with corners
$ Gamma ackslash X _0 subset Gamma ackslash X $. In fact, we prove that
$ Gamma ackslash X _0 $ is a realization (under a natural piecewise analytic diffeomorphism) of
$ Gamma ackslash overline{X} $ inside the interior
$ Gamma ackslash X $. For application to the theory of harmonic maps and geometric rigidity, we prove this retraction and diffeomorphism have finite energy except for a few low ranks examples. We also use tilings to give an explicit description of a cofinal family of neighborhoods of a face of
$ Gamma ackslash overline{X} $, and study the dependance of tilings on the parameter b and the degeneration of tilings.