PAOLO DE DONATO

Dottore di ricerca

ciclo: XXXV


supervisore: E. Spadaro
relatore: E. Spadaro

Titolo della tesi: Rectifiability of stationary varifolds branching set with multiplicity at most 2

This thesis deals with regularity and rectifiability properties on the branching set of stationary varifolds that can be represented as the graph of a two-valued function. In the first chapter I briefly show the Simon and Wickramasekera’s work in which they introduce a frequency function monotonicity formula for two-valued $C^{1,\alpha}$ functions with stationary graph that leads to an estimate of the Hausdorff dimension of the branching set. In the second chapter I build upon Simon and Wickramasekera’s work and introduce several relaxed frequency functions in order to get an estimat of the Minkowski’s content of the branching set. I then use their result to prove the local (n − 2)-rectifiablility of the branching set.

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