Height estimate and slicing formulas in the Heisenberg group

Abstract

We prove a height estimate (distance from the tangent hyperplane) for $\Lambda$-minimizers of the perimeter in the sub-Riemannian Heisenberg group. The estimate is in terms of a power of the excess ($L^2$-mean oscillation of the normal) and its proof is based on a new coarea formula for rectifiable sets in the Heisenberg group.