论文标题
Lipschitz可不同的空间上的抽象和混凝土切线模块
Abstract and concrete tangent modules on Lipschitz differentiability spaces
论文作者
论文摘要
我们构建了一个从Gigli的抽象切线模块的等距嵌入到一个空间的混凝土切线模块中，该模块容纳了（弱）Lipschitz可区分结构，并给出两个等效条件，这些条件是嵌入是同构时的表征。加上Bate-kangasniemi-orponen最近的一篇文章中的论点，该等效性用于表明$ {\ rm lip} - {\ rm lip} $ -Type条件$ {\ rm lip} f \ le c | df | $的存在对$ lipschitz的存在对$ chits的存在，以及$ chitschitz的存在，以及$ chitschitz的结构{ lip} f = | df | $。 我们还提供了Gigli和第二作者的结果的直接证明，对于具有强烈校正分解的空间，Gigli的切线模块承认，等距嵌入了所谓的Gromov-Hausdorff切线模块，而没有任何先验反射性假设。
We construct an isometric embedding from Gigli's abstract tangent module into the concrete tangent module of a space admitting a (weak) Lipschitz differentiable structure, and give two equivalent conditions which characterize when the embedding is an isomorphism. Together with arguments from a recent article by Bate--Kangasniemi--Orponen, this equivalence is used to show that the ${\rm Lip}-{\rm lip}$ -type condition ${\rm lip} f\le C|Df|$ implies the existence of a Lipschitz differentiable structure, and moreover self-improves to ${\rm lip} f =|Df|$. We also provide a direct proof of a result by Gigli and the second author that, for a space with a strongly rectifiable decomposition, Gigli's tangent module admits an isometric embedding into the so-called Gromov--Hausdorff tangent module, without any a priori reflexivity assumptions.
