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Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs. (English) Zbl 1188.53027

The authors consider \(\mathbb H\)-regular graphs, a class of intrinsic regular hypersurfaces in the Heisenberg group \({\mathbb H}^n={\mathbb C}^n\times {\mathbb R}\) endowed with a left invariant metric \(d_\infty\) equivalent to its Carnot Caratheodory metric. They obtain the following geometric properties: a uniqueness result for \(\mathbb H\)-regular graphs of prescribed horizontal normal as well as their regularity as long as there is regularity on the horizontal normal. These results contribute to the study of further geometric properties of this class graph.

MSC:

53C17 Sub-Riemannian geometry
35L60 First-order nonlinear hyperbolic equations
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
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