论文标题
本地Minkowski空间上的规范无限的希尔伯特式结构
A canonical infinitesimally Hilbertian structure on locally Minkowski spaces
论文作者
论文摘要
本文的目的是显示在本地Minkowski公制量$ $（\ MATHSF X，\ MATHSF D，\ MATHFRAK M）$上定义的规范距离$ \ Mathsf d'U $的存在。 i）$ \ MATHSF D'U $等于$ \ Mathsf D $， ii）$（\ MATHSF X，\ MATHSF D'，\ MATHFRAK M）$是无限的Hilbertian。 在$（\ Mathsf X，\ Mathsf D，\ Mathfrak m）上，这种新的规律性假设本质上是迫使该结构与Minkowski空间相似，并定义了包括所有Finsler歧管的一类度量测量结构，实际上严格更大。所需的距离$ \ mathsf d'U $将是与所谓的Korevaar-Schoen Energy关联的固有距离$ \ Mathsf D_ \ Mathsf {KS} $，这被证明是二次形式。特别是，我们表明与度量度量空间相关的Cheeger能量$（\ Mathsf X，\ Mathsf D_ \ Mathsf {KS}，\ Mathfrak M）$实际上是Korevaar-Schoen Energy。
The aim of this paper is to show the existence of a canonical distance $\mathsf d'$ defined on a locally Minkowski metric measure space $(\mathsf X,\mathsf d,\mathfrak m)$ such that: i) $\mathsf d'$ is equivalent to $\mathsf d$, ii) $(\mathsf X, \mathsf d', \mathfrak m)$ is infinitesimally Hilbertian. This new regularity assumption on $(\mathsf X, \mathsf d,\mathfrak m)$ essentially forces the structure to be locally similar to a Minkowski space and defines a class of metric measure structures which includes all the Finsler manifolds, and it is actually strictly larger. The required distance $\mathsf d'$ will be the intrinsic distance $\mathsf d_\mathsf{KS}$ associated to the so-called Korevaar-Schoen energy, which is proven to be a quadratic form. In particular, we show that the Cheeger energy associated to the metric measure space $(\mathsf X, \mathsf d_\mathsf{KS}, \mathfrak m)$ is in fact the Korevaar-Schoen energy.
