Height estimate and slicing formulas in the Heisenberg group

We prove a height-estimate (distance from the tangent hyperplane) for $Λ$-minima 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.

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