A proof by calibration of an isoperimetric inequality in the Heisenberg group \({\mathbb{H}^n}\)



Let D be a closed disk centered at the origin in the horizontal hyperplane {t = 0} of the sub-Riemannian Heisenberg group \({\mathbb{H}^n}\), and C the vertical cylinder over D. We prove that the perimeter of any set E such that \({D\subset E\subset C}\) 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).

Mathematics Subject Classification (2000)

53C17 53C42 49Q20 


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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaEspaña

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