Calculus of Variations and Geometric Measure Theory

D. Barilari - U. Boscain - D. Cannarsa

On the induced geometry on surfaces in 3D contact sub-Riemannian manifolds

created by barilari on 28 Sep 2020



Inserted: 28 sep 2020

Pages: 24
Year: 2020

ArXiv: 2009.11748 PDF


Given a surface $S$ in a 3D contact sub-Riemannian manifold $M$, we investigate the metric structure induced on $S$ by $M$, in the sense of length spaces. First, we define a coefficient $\widehat K$ at characteristic points that determines locally the characteristic foliation of $S$. Next, we identify some global conditions for the induced distance to be finite. In particular, we prove that the induced distance is finite for surfaces with the topology of a sphere embedded in a tight coorientable distribution, with isolated characteristic points.