论文标题
在度量空间中本质上的Hölder部分
Intrinsically Hölder sections in metric spaces
论文作者
论文摘要
我们引入了公制空间中本质上的Hölder图的概念。根据Le Donne和作者的最新论文，我们证明了一些相关的结果，因为Ascoli-arzelàCompactness定理，Ahlfors-David的规律性以及此类部分的扩展定理。在本说明的第一部分中，借助Cheeger理论，我们定义了合适的集合，以便在$ \ r $或$ \ c上获得矢量空间，$ convex set和与本质上Hölder图的等价关系。在Lipschitz案例中，这最后三个属性也是新的。在整个论文中，我们都使用基本的数学工具。
We introduce a notion of intrinsically Hölder graphs in metric spaces. Following a recent paper of Le Donne and the author, we prove some relevant results as the Ascoli-Arzelà compactness Theorem, Ahlfors-David regularity and the Extension Theorem for this class of sections. In the first part of this note, thanks to Cheeger theory, we define suitable sets in order to obtain a vector space over $\R$ or $\C,$ a convex set and an equivalence relation for intrinsically Hölder graphs. These last three properties are new also in the Lipschitz case. Throughout the paper, we use basic mathematical tools.
