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The regularity and existence of branched minimal submanifolds

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If you have a question about this talk, please contact Jonathan Ben-Artzi.

Multivalued functions arise naturally in the study of the branch set of branched minimal immersions. Simon and Wickramasekera (2007) showed how to construct a large class of multivalued solutions in C1,μ to the Dirichlet problem for the minimal surface equation provided the boundary data satisfied a k-fold symmetry condition. I will show that the branch sets of the minimal hypersurfaces they constructed are real analytic submanifolds, which involves proving a general regularity result for multivalued solutions to elliptic equations. I also extend their existence result, which was specific to the minimal surface equation, to show that there exists multivalued solutions in C1,μ to other elliptic equations and to elliptic systems that preserve the k-fold symmetry condition.

This talk is part of the Partial Differential Equations seminar series.

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