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The Caffarelli–Kohn–Nirenberg inequality on metric measure spaces
manuscripta mathematica ( IF 0.5 ) Pub Date : 2020-06-02 , DOI: 10.1007/s00229-020-01206-1
Willian Tokura , Levi Adriano , Changyu Xia

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Caffarelli–Kohn–Nirenberg inequality with the same exponent $$n(n\ge 2)$$ n ( n ≥ 2 ) , then it has exactly n -dimensional volume growth. As application, we obtain geometric and topological properties of Alexandrov spaces, Riemannian manifolds and Finsler manifolds which support a Caffarelli–Kohn–Nirenberg inequality.

中文翻译:

度量空间上的 Caffarelli-Kohn-Nirenberg 不等式

在本文中,我们证明,如果度量空间满足体积倍增条件和 Caffarelli-Kohn-Nirenberg 不等式且指数相同 $$n(n\ge 2)$$n ( n ≥ 2 ) ,则它有正好是 n 维体积增长。作为应用,我们获得了支持 Caffarelli-Kohn-Nirenberg 不等式的 Alexandrov 空间、黎曼流形和 Finsler 流形的几何和拓扑性质。
更新日期:2020-06-02
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