关于黎曼流形间拟正则映射的注记
Notes on quasiregular maps between Riemannian manifolds
摘要：
这些注记提供了一个阐述获得著名的标准结果的拟正则映射的黎曼流形，鉴于相应的理论在欧几里德设置。我们回顾了几种不同的方法，一阶Sobolev空间之间的黎曼流形，并表明，它们导致等价的定义准正则映射。我们解释如何，例如Reshetnyak定理，度和局部指数理论，和准正规的变量变量变换公式转移到流形设置从欧几里得空间。最后，我们证明了拟正则映射的拉回保持共形指数的Sobolev微分形式
英文摘要：
These notes provide an exposition on obtaining the well-known standard results of quasiregular maps on Riemannian manifolds, given the corresponding theory in the Euclidean setting. We recall several different approaches to first-order Sobolev spaces between Riemannian manifolds, and show that they result in equivalent definitions of quasiregular maps. We explain how e.g. Reshetnyak's theorem, degree and local index theory, and the quasiregular change of variables formula are transferred into the manifold setting from Euclidean spaces. Finally, we conclude with a proof of the basic fact that pull-backs with quasiregular maps preserve Sobolev differential forms of the conformal exponent
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