This volume covers contemporary aspects of geometric measure theory with a focus on
applications to partial differential equations free boundary problems and water waves. It is
based on lectures given at the 2019 CIME summer school Geometric Measure Theory and
Applications - From Geometric Analysis to Free Boundary Problems which took place in Cetraro
Italy under the scientific direction of Matteo Focardi and Emanuele Spadaro. Providing a
description of the structure of measures satisfying certain differential constraints and
covering regularity theory for Bernoulli type free boundary problems and water waves as well as
regularity theory for the obstacle problems and the developments leading to applications to the
Stefan problem this volume will be of interest to students and researchers in mathematical
analysis and its applications.
