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      Wick rotations of solutions to the minimal surface equation, the zero mean curvature equation and the Born-Infeld equation

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          Abstract

          In this paper we investigate relations between solutions to the minimal surface equation in Euclidean \(3\)-space \(\mathbb{E}^3\), the zero mean curvature equation in Lorentz-Minkowski \(3\)-space \(\mathbb{L}^3\) and the Born-Infeld equation under Wick rotations. We prove that the existence conditions of real solutions and imaginary solutions after Wick rotations are written by symmetries of solutions, and reveal how real and imaginary solutions are transformed under Wick rotations. We also give a transformation theory for zero mean curvature surfaces containing lightlike lines with some symmetries. As an application, we give new correspondences among some solutions to the above equations by using the non-commutativity between Wick rotations and isometries in the ambient space.

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          Maximal surfaces with singularities in Minkowski space

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            Maximal surfaces with conelike singularities

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              Generalized maximal surfaces in Lorentz–Minkowski space L3

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                Author and article information

                Journal
                01 November 2017
                Article
                1711.00299
                1d6c9330-4a20-4ebd-ae6b-00755d43b7f8

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                53A10 (Primary), 58J72, 53B30 (Secondary)
                18 pages, 4 figures
                math.DG

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