具有伸缩的拟度量空间的代数和解析性质
Algebraic and analytic properties of quasimetric spaces with dilations
摘要：
本文给出了正则次黎曼流形的局部切锥理论和这类空间之间映射的可微性的公理化方法。这种公理化的方法依赖于一个膨胀结构的概念，这是在准度量空间的一般框架中引入的。考虑准度量使我们能够覆盖一般情况下，特别是，最小的光滑性假设的向量场定义的子黎曼结构。值得注意的是，现有的度量空间的理论不能直接推广到拟度量空间。
英文摘要：
We provide an axiomatic approach to the theory of local tangent cones of regular sub-Riemannian manifolds and the differentiability of mappings between such spaces. This axiomatic approach relies on a notion of a dilation structure which is introduced in the general framework of quasimetric spaces. Considering quasimetrics allows us to cover a general case including, in particular, minimal smoothness assumptions on the vector fields defining the sub-Riemannian structure. It is important to note that the theory existing for metric spaces can not be directly extended to quasimetric spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
