Calculus of Variations and Geometric Measure Theory
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F. Bigolin - F. Serra Cassano

Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non linear first-order PDEs

created by bigolin on 26 Oct 2007
modified on 29 Jun 2009

[BibTeX]

Accepted Paper

Inserted: 26 oct 2007
Last Updated: 29 jun 2009

Journal: Adv. Calc. Var.
Year: 2009

Abstract:

We continue the study about $H$- regular graphs, a class of intrinsic regular hypersurfaces in the Heisenberg group $H^n=C^n \times R\equiv R^{2n+1}$ endowed with a left- invariant metric $d_{\infty}$ equivalent to its Carnot- Carathéodory metric. Here we investigate their relationships with suitable weak solutions of nonlinear first- order PDEs. As a consequence we infer some of their geometric properties as an uniqueness result for $H$- regular graphs of prescribed horizontal normal as well as their (Euclidean) regularity provided regularity on the horinzontal normal.

Keywords: intrinsic regular hypersurfaces in the Heisenberg group


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