论文标题
通过凸三角学上的左不变子 - 菲因斯勒在海森堡组上的大地测量表的显式公式
Explicit formulae for geodesics in left invariant sub-Finsler problems on Heisenberg groups via convex trigonometry
论文作者
论文摘要
在本文中，我们在Heisenberg组上的某些剩余的子芬斯勒问题$ \ mathbb {h} _ {2n+1} $中获得了大地测量学的显式公式。我们的主要假设是：在身份处的紧凑型单位速度集合允许球形坐标的概括。这包括凸面和坐标二维集合的总和，所有左右不变的子 - 里工级结构上的$ \ mathbb {h} _ {2n+1} $以及$ l_p $ -mmetric的单位球，均为$ 1 \ le p \ le p \ le p \ le p \ le p \ le \ le \ iffty $。在最后一个情况下，根据第一种不完整的Euler积分获得了极端。
In the present paper, we obtain explicit formulae for geodesics in some left-invariant sub-Finsler problems on Heisenberg groups $\mathbb{H}_{2n+1}$. Our main assumption is the following: the compact convex set of unit velocities at identity admits a generalization of spherical coordinates. This includes convex hulls and sums of coordinate 2-dimensional sets, all left-invariant sub-Riemannian structures on $\mathbb{H}_{2n+1}$, and unit balls in $L_p$-metric for $1\le p\le\infty$. In the last case, extremals are obtained in terms of incomplete Euler integral of the first kind.
