Abstract
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 Lp–metric for $1\le p\le \infty $ . In the last case, extremals are obtained in terms of incomplete Euler integral of the first kind.
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