A negative answer to a one-dimensional symmetry problem in the Heisenberg group
classification
🧮 math.AP
keywords
groupheisenbergalonganswerboundedcenterconjectureconjectured
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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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