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A negative answer to a one-dimensional symmetry problem in the Heisenberg group

I. Birindelli·E. Lanconelli
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Abstract

De Giorgi conjectured that bounded monotone solutions to the Ginzburg-Landau equation are constant along hyperplanes, in this paper we prove that in the Heisenberg group this conjecture doesn't hold true with respect to the center direction.

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I. Birindelli, E. Lanconelli. 2001-08-29. A negative answer to a one-dimensional symmetry problem in the Heisenberg group. https://arxiv.org/abs/math/0108198

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