The classification of complete stable area-stationary surfaces in the Heisenberg group $\mathbb{H}^1$

Details The classification of complete stable area-stationary surfaces in the Heisenberg group $\mathbb{H}^1$ The classification of complete stable area-stationary surfaces in the Heisenberg group $\mathbb{H}^1$

2008-10-29

arxiv.org/abs/0810.5249v4

Mathematics

Differential Geometry

32 pages, no figures, added reference missed in version 3

Scientific paper

We prove that any $C^2$ complete, orientable, connected, stable
area-stationary surface in the sub-Riemannian Heisenberg group $\mathbb{H}^1$
is either a Euclidean plane or congruent to the hyperbolic paraboloid $t=xy$.

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