Nonminimality of spirals in sub-Riemannian manifolds
Differential Geometry
2021-01-27 v1 Metric Geometry
Abstract
We show that in analytic sub-Riemannian manifolds of rank 2 satisfying a commutativity condition spiral-like curves are not length minimizing near the center of the spiral. The proof relies upon the delicate construction of a competing curve.
Keywords
Cite
@article{arxiv.2101.10940,
title = {Nonminimality of spirals in sub-Riemannian manifolds},
author = {Roberto Monti and Alessandro Socionovo},
journal= {arXiv preprint arXiv:2101.10940},
year = {2021}
}