On energy functional in sub-Finsler geometry

This paper investigates critical points of the energy functional in sub-Finsler manifolds. Critical points of the energy functional correspond to sub-Finsler geodesics, i.e., horizontal curves that are extremal for the energy, emphasizing their importance in sub-Finsler geometry. Assuming that the sub-Finsler metric is bumpy (in the Morse–Bott sense), the energy functional on the free loop space has the Morse--Bott property, and we establish a direct link between critical points and closed geodesics. We shed light on the existence of at least one closed geodesic on compact sub-Finsler manifolds.