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.
|頁（從 - 到）||811-821|
|期刊||Proceedings of the American Mathematical Society|
|出版狀態||已出版 - 2012|