PRIVILEGED COORDINATES FOR CARNOT-CARATHEODORY SPACES OF LOWER SMOOTHNESS

Basalaev S. G.

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PRIVILEGED COORDINATES FOR CARNOT-CARATHEODORY SPACES OF LOWER SMOOTHNESS

机译：较低光滑度的Carnot-Caratheodory空间的特权坐标

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摘要

We describe classes of local coordinates on the Carnot-Caratheodory 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.

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来源
《Siberian Mathematical Journal》 |2020年第5期|共15页
作者
Basalaev S. G.;
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作者单位

Novosibirsk State Univ Sobolev Inst Math Novosibirsk Russia;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
sub-Riemannian geometry; nilpotent tangent cone; privileged coordinates;

机译：子riemannian几何;尼洛Potent锥;特权坐标;

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1. ON　k-Smooth,k-Very　Smooth　and　K-Strongly　Smooth　Banach　Spaces [J] . 哈尔滨工业大学学报：英文版 . 1998,第001期
2. Normal Ordering Expansion of Hermite Polynomials of Radial Coordinate Operator in Three-Dimensional Coordinate Space [J] . SHAO Yu-Chong, FAN Hong-Yi 理论物理通讯：英文版 . 2008,第004期
3. Smoothness spaces of higher order on lower dimensional subsets of the Euclidean space [J] . Ihnatsyeva Lizaveta, Korte Riikka Mathematische Nachrichten . 2015,第11a12期

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4. LOWER BOUNDS FOR THE NUMBER OF VECTORS WITH ALGEBRAIC COORDINATES NEAR SMOOTH SURFACES [J] . Journal of neurosurgical sciences . 2020,第1期

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6. On controlling privileged vehicles by means of coordinated traffic lights [C] . Di Febbraro, A., Giglio, . 2003

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7. The Production of a Privileged Space: Boundaries, Esthetics and the Legitimation of Social Differences in Medellin, Colombia [D] . Gutiérrez, Lina Maria Villegas. 2017

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8. The Privileged Chemical Space Predictor (PCSP): A computer program that identifies privileged chemical space from screens of modularly assembled chemical libraries [O] . Steven J. Seedhouse, Lucas P. Labuda, Matthew D. Disney -1

机译：特权化学空间预测器（pCsp）：一种计算机程序它从模块化组装化学文库的屏幕识别特权化学空间
9. Smoothness spaces of higher order on lower dimensional subsets of the Euclidean space [O] . Ihnatsyeva, Lizaveta, Korte, Riikka 2011

机译：低维子集上的高阶光滑空间欧几里德空间
10. Carnot-Caratheodory Spaces Seen from Within [R] . Gromov, M. 1994

机译：内部看到的卡诺 - Caratheodory空间

PRIVILEGED COORDINATES FOR CARNOT-CARATHEODORY SPACES OF LOWER SMOOTHNESS

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