A proof by calibration of an isoperimetric inequality in the Heisenberg group Hn

Let D be a closed disk centered at the origin in the horizontal hyperplane {t = 0} of the sub- Riemannian Heisenberg group H-n, and C the vertical cylinder over D. We prove that the perimeter of any set E such that D subset of E subset of C is larger than or equal to the one of the rotationally symmetric sphere with constant mean curvature of the same volume, and that equality holds only for these spheres using a recent result by Monti and Vittone (Math Z 1-17, 2010).