Non-minimality of spirals in sub-Riemannian manifolds
نویسندگان
چکیده
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 spiral. The proof relies upon delicate construction competing curve.
منابع مشابه
Corners in Non-equiregular Sub-riemannian Manifolds
We prove that in a class of non-equiregular sub-Riemannian manifolds corners are not length minimizing. This extends the results of [4]. As an application of our main result we complete and simplify the analysis in [6], showing that in a 4-dimensional subRiemannian structure suggested by Agrachev and Gauthier all length-minimizing curves are smooth.
متن کاملHausdorff volume in non equiregular sub-Riemannian manifolds
In this paper we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it with a smooth volume. We first give the Lebesgue decomposition of the Hausdorff volume. Then we study the regular part, show that it is not commensurable with the smooth volume, and give conditions under which it is a Radon measure. We finally give a complete characterization of the singul...
متن کاملHausdorff measures and dimensions in non equiregular sub-Riemannian manifolds
This paper is a starting point towards computing the Hausdorff dimension of submanifolds and the Hausdorff volume of small balls in a sub-Riemannian manifold with singular points. We first consider the case of a strongly equiregular submanifold, i.e., a smooth submanifold N for which the growth vector of the distribution D and the growth vector of the intersection of D with TN are constant on N...
متن کاملOn Sublaplacians of Sub-riemannian Manifolds
In this note we address a notion of sublaplacians of sub-Riemannian manifolds. In particular for fat sub-Riemannian manifolds we answered the sublaplacian question proposed by R. Montgomery in [21, p.142]
متن کاملThe Geometry of Sub-riemannian Three-manifolds
The local equivalence problem for sub-Riemannian structures on threemanifolds is solved. In the course of the solution, it is shown how to attach a canonical Riemannian metric and connection to the given sub-Riemannian metric and it is shown how all of the differential invariants of the sub-Riemannian structure can be calculated. The relation between the completeness of the sub-Riemannian metri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2021
ISSN: ['0944-2669', '1432-0835']
DOI: https://doi.org/10.1007/s00526-021-02077-4