End-Point Equations and Regularity of Sub-Riemannian Geodesics |
| |
Authors: | Gian Paolo Leonardi Roberto Monti |
| |
Affiliation: | (1) Dipartimento di Matematica Pura ed Applicata, Università di Modena e Reggio Emilia, Via Campi, 213/b, 41100 Modena, Italy;(2) Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Trieste, 63, 35121 Padova, Italy |
| |
Abstract: | For a large class of equiregular sub-Riemannian manifolds, we show that length-minimizing curves have no corner-like singularities. Our first result is the reduction of the problem to the homogeneous, rank-2 case, by means of a nilpotent approximation. We also identify a suitable condition on the tangent Lie algebra implying existence of a horizontal basis of vector fields whose coefficients depend only on the first two coordinates x 1, x 2. Then, we cut the corner and lift the new curve to a horizontal one, obtaining a decrease of length as well as a perturbation of the end-point. In order to restore the end-point at a lower cost of length, we introduce a new iterative construction, which represents the main contribution of the paper. We also apply our results to some examples. Received: July 2006, Revision: October 2006, Accepted: November 2006 |
| |
Keywords: | KeywordHeading" > and phrases: Sub-Riemannian geodesics regularity of length minimizers nilpotent approximation |
本文献已被 SpringerLink 等数据库收录! |
|