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

Rosales, Leobardo
September 2010
Calculus of Variations & Partial Differential Equations;Sep2010, Vol. 39 Issue 1/2, p59
Academic Journal
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 C1, 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 C1, α stable branched immersed minimal surfaces, with a certain evenness symmetry.


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