Existence and properties of minimal surfaces and varifolds with contact angle conditions

This thesis is devoted to the study of minimal surfaces with prescribed angle conditions and to their generalizations in the sense of Geometric Measure Theory. In the first part we study boundary properties of varifolds with contact angle conditions such as bounded first variation, monotonicity formulae and rectifiability. In the second one, using min-max techniques, we prove existence and regularity of minimal surfaces in compact domains which meet the boundary of the container with a fixed angle.