Carnot-Carathéodory测地线切线的存在性
Existence of tangent lines to Carnot-Carathéodory geodesics
摘要：
证明了Carnot-Carathéodory空间中的长度极小曲线在任意点上至少有一条正切曲线（即，幂零近似中的爆破）等于直的水平线。这是长度最小化器的第一个规律性结果，该结果在空间上没有任何假设（例如，它的排名，步骤，或解析性）或曲线，它是新颖的，甚至在卡诺集团的设置。
英文摘要：
We show that length minimizing curves in Carnot-Carathéodory spaces possess at any point at least one tangent curve (i.e., a blow-up in the nilpotent approximation) equal to a straight horizontal line. This is the first regularity result for length minimizers that holds with no assumption on either the space (e.g., its rank, step, or analyticity) or the curve, and it is novel even in the setting of Carnot groups.
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。
