## PAOLO DE DONATO

PhD Graduate**PhD program:**: XXXV

**supervisor**: E. Spadaro

**advisor**: E. Spadaro

**Thesis title:**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.