The CR-Volume of Horizontal Submanifolds of Spheres

Abstract: We study an analog in CR-geometry of the conformal volume of Li-Yau. In particular, to submanifolds of odd-dimensional spheres that are Legendrian or, more generally, horizontal with respect to the sphere's standard CR-structure we associate a quantity that is invariant under the CR-automorphisms of the sphere. We apply this concept to a corresponding notion of Willmore energy.