# Talk

Modul:   MAT673  Seminar PDE and Mathematical Physics

## Fine structure and higher regularity of the branch sets

Dr. Brian Krummel talk

Speaker invited by: Prof. Dr. Camillo De Lellis

Date: 30.04.15  Time: 18.15 - 19.15  Room: Y27H35/36

I will discuss work on the fine structure and higher regularity of the branch set of two-valued solutions to the Laplace's equation and the minimal surface system. In joint work with Neshan Wickramasekera, we have shown that the branch set are countably $(n-2)$-rectifiable. In independent work, I have shown that the branch set is locally real analytic on a relatively open dense subset of the branch set. Essential ingredients for both results are the monotonicity formula for frequency functions due to F. J. Almgren and a blow-up method, which was originally applied by Leon Simon to multiplicity one classes of minimal submanifolds.