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

  • Leobardo RosalesEmail author
Article

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.

Mathematics Subject Classification (2000)

49Q05 49Q15 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Rice UniversityHoustonUSA

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