Functional geometric method for solving free boundary problems for harmonic functions

摘要

Abstract. A survey is given of results and approaches for a broad spectrum of free boundary problems for harmonic functions of two variables. The main results are obtained by the functional geometric method. The core of these methods is an interrelated analysis of the functional and geometric characteristics of the problems under consideration and of the corresponding non-linear Riemann–Hilbert problems. An extensive list of open questions is presented.