Seminar Analysis: Davide Vittone (University of Padua)

Area-minimizing graphs in the Heisenberg group

We consider the area functional for graphs in the sub-Riemannian Heisenberg group and study minimizers of the associated Dirichlet problem. We prove that,under a bounded slope condition on the boundary datum, there exists a unique minimizer and that this minimizer is Lipschitz continuous. We also provide an example showing that, in the first Heisenberg group, Lipschitz regularity cannot be improved even under the bounded slope condition. This is based on a joint work with A. Pinamonti, F. SerraCassano and G. Treu.

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