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The geometric structure of solutions to the two-valued minimal surface equation

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Abstract

Recently, Simon and Wickramasekera (J Differ Geom 75:143–173, 2007) introduced a PDE method for producing examples of stable branched minimal immersions in \({\mathbb{R}^{3}}\). This method produces two-valued functions u over the punctured unit disk in \({\mathbb{R}^{2}}\) so that either u cannot be extended continuously across the origin, or G the two-valued graph of u is a C 1,α stable branched immersed minimal surface. The present work gives a more complete description of these two-valued graphs G in case a discontinuity does occur, and as a result, we produce more examples of C 1,α stable branched immersed minimal surfaces, with a certain evenness symmetry.

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  1. Rice University, MS 136 6100 S. Main St., Houston, TX, 77005-1892, USA

    Leobardo Rosales

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  1. Leobardo Rosales
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Correspondence to Leobardo Rosales.

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Communicated by L. Simon.

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Rosales, L. The geometric structure of solutions to the two-valued minimal surface equation. Calc. Var. 39, 59–84 (2010). https://doi.org/10.1007/s00526-009-0301-y

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  • DOI: https://doi.org/10.1007/s00526-009-0301-y

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