Mappings of finite distortion between metric measure spaces
Mappings of finite distortion between metric measure spaces
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度量测度空间之间的有限畸变映射
DOI：
10.1090/ecgd/277
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Chang
中科院分区：
文献类型：
--
作者：
Chang
我们建立了支持 (1, 1)-Poincaré 不等式的真 Ahlfors 正则度量测度空间之间的有限畸变映射的基本分析性质。作为应用，我们证明在畸变函数一定的可积性假设下，A型广义n流形之间的有限畸变映射的分支集具有零Hausdorff n测度。
We establish the basic analytic properties of mappings of finite distortion between proper Ahlfors regular metric measure spaces that support a (1, 1)-Poincaré inequality. As applications, we prove that under certain integrability assumption for the distortion function, the branch set of a mapping of finite distortion between generalized n-manifolds of type A has zero Hausdorff n-measure.