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- Title
Surfaces of genus g ≥ 1 in 3D contact sub-Riemannian manifolds.
- Authors
Bellini, Eugenio; Boscain, Ugo
- Abstract
We consider smooth embedded surfaces in a 3D contact sub-Riemannian manifold and the problem of the finiteness of the induced distance (i.e., the infimum of the length of horizontal curves that belong to the surface). Recently it has been proved that for a surface having the topology of a sphere embedded in a tight co-orientable structure, the distance is always finite. In this paper we study closed surfaces of genus larger than 1, proving that such surfaces can be embedded in such a way that the induced distance is finite or infinite. We then study the structural stability of the fmiteness/not-finiteness of the distance.
- Subjects
STRUCTURAL stability; TOPOLOGY; SPHERES; RIEMANNIAN manifolds
- Publication
ESAIM: Control, Optimisation & Calculus of Variations, 2023, Vol 29, p1
- ISSN
1292-8119
- Publication type
Article
- DOI
10.1051/cocv/2023072