The regularity and existence of branched minimal submanifolds

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• Brian Krummel (DPMMS)
• Monday 16 January 2012, 16:00-17:00
• CMS, MR14.

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 C^1,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 C^1,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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