A proof by calibration of an isoperimetric inequality in the Heisenberg group H^n

Details A proof by calibration of an isoperimetric inequality in the Heisenberg group H^n A proof by calibration of an isoperimetric inequality in the Heisenberg group H^n

2008-03-09

arxiv.org/abs/0803.1313v3

Mathematics

Differential Geometry

Final version. To appear in Calc. Var. Partial Differential Equations

Scientific paper

Let $D$ be a closed disk centered at the origin in the horizontal hyperplane $\{t=0\}$ of the sub-Riemannian Heisenberg group $\hh^n$, and $C$ the vertical cylinder over $D$. We prove that any finite perimeter set $E$ such that $D\subset E\subset C$ has perimeter 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 the spheres using a recent result by Monti and Vittone [12].

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