In [11] it is proved that length-minimizing curves in Carnot groups have infinitesimal excess at any point, for a suitable sequence of scales. In this paper we prove some results dealing with the small excess regime. We prove a height-estimate for horizontal curves and an approximation of geodesics with Lipschitz graphs along the direction where excess is small. The setting is that of free Carnot groups.
HEIGHT ESTIMATE AND LIPSCHITZ APPROXIMATION FOR GEODESICS IN CARNOT GROUPS
Monti, R;Zaccaron, M
2020
Abstract
In [11] it is proved that length-minimizing curves in Carnot groups have infinitesimal excess at any point, for a suitable sequence of scales. In this paper we prove some results dealing with the small excess regime. We prove a height-estimate for horizontal curves and an approximation of geodesics with Lipschitz graphs along the direction where excess is small. The setting is that of free Carnot groups.
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