标题： 二步幂零黎曼李群的渐进行为 显示英文标题

标题： Asymptotics of Riemannian Lie groups with nilpotency step 2

摘要： 我们推导出比较渐近黎曼或次黎曼度量的估计，在二步幂零李群中。 给定一个次黎曼度量，我们构造一个Carnot度量，其平方与原度量的平方保持在有界距离内。 作为结果，我们得到了(次)黎曼度量球体积渐近展开中误差项的改进估计。 为了实现这一点，我们开发了一种新的技术来扰动次黎曼测地线，使我们能够在指定的垂直方向上修改它们的端点。 显示英文摘要

摘要： We derive estimates comparing asymptotic Riemannian or sub-Riemannian metrics in step-2 nilpotent Lie groups. Given a sub-Riemannian metric, we construct a Carnot metric whose square remains at a bounded distance from the square of the original metric. As a consequence, we obtain a refined estimate of the error term in the asymptotic expansion of the volume of (sub-)Riemannian metric balls. To achieve this, we develop a novel technique to perturb sub-Riemannian geodesics, allowing us to modify their endpoints in a prescribed vertical direction.