Calculus of Variations and Geometric Measure Theory
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R. Monti - M. Rickly

Convex isoperimetric sets in the Heisenberg group

created by monti on 26 Jul 2006
modified on 27 Oct 2008


Accepted Paper

Inserted: 26 jul 2006
Last Updated: 27 oct 2008

Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci.
Year: 2008


We characterize convex isoperimetric sets in the Heisenberg group endowed with horizontal perimeter. We first prove Sobolev regularity for a certain class of R2-valued vector fields of bounded variation in the plane related to the curvature equations. Then, by an approximation-reparameterization argument, we show that the boundary of convex isoperimetric sets is foliated by geodesics of the Carnot-Carathéodory distance.


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