Privileged Coordinates for Carnot–Carathéodory Spaces of Lower Smoothness
[摘要] We describe classes of local coordinates on the Carnot–Carathéodory spaces of lower smoothness which permit the homogeneous approximation of quasimetrics and basis vector fields. We establish the minimal smoothness that is required for these classes to coincide with the class of the already-described privileged coordinates in the infinite smoothness case. Moreover, we apply these results to prove the analogs of the available theorems in the case of the canonical coordinates of the second kind. Also, we prove some convergence theorems in quasimetric spaces.
[发布日期] [发布机构]
[效力级别] [学科分类] 数学（综合）
[关键词] sub-Riemannian geometry;nilpotent tangent cone;privileged coordinates [时效性]
