The classification of complete stable area-stationary surfaces in the Heisenberg group mathbb{H}¹
classification
🧮 math.DG
math.MG
keywords
area-stationarycompletegroupheisenbergmathbbstableclassificationcongruent
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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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