Description
Sub-Riemannian geometry is a generalization of Riemannian geometry in which a metric is defined only on a subset of preferred directions, called a distribution. For curves tangent to the distribution, one can define their length, and the curves that minimize length are called sub-Riemannian geodesics. In this talk, I will discuss the regularity of sub-Riemannian geodesics: whereas geodesics in Riemannian geometry are always smooth, sub-Riemannian geodesics are not always smooth. I will also present examples showing that sub-Riemannian geodesics can branch. This is based on joint work in progress with A. Schiavoni Piazza and A. Socionovo.
