The Hessian of the distance from a surface in the Heisenberg group

Abstract

We compute the horizontal Hessian of the signed Carnot-Charatheodory distance from a surface S in the Heisenberg group H. The expression for the Hessian is in terms of the surface's intrinsic curvatures. As an application, we compute the horizontal Hessian of the Carnot-Charatheodory distance from a point in H.

References in corpus (2)

• The Bernstein Problem in the Heisenberg Group
• H-minimal graphs of low regularity in the Heisenberg group

Cited by in corpus (1)

• CC-distance and metric normal of smooth hypersurfaces in sub-Riemannian Carnot groups