The problem of the local summability of the sub-Riemannian mean curvature H of a hypersurface M in the Heisenberg group, or in more general Carnot groups, near the characteristic set of M arises naturally in several questions in geometric measure theory. We construct an example which shows that the sub-Riemannian mean curvature H of a C2 surface M in the Heisenberg group H1 in general fails to be integrable with respect to the Riemannian volume on M.
- First and second variation
- H-mean curvature
- Integration by parts
- Minimal surfaces
- Monotonicity of the H-perimeter