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 (3)

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

Cited by in corpus (5)

• Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg group
• CC-distance and metric normal of smooth hypersurfaces in sub-Riemannian Carnot groups
• Tubular neighborhoods in the sub-Riemannian Heisenberg groups
• Heat content and horizontal mean curvature on the Heisenberg group
• Rigidity results for non local phase transitions in the Heisenberg group $H$