Progress in Surface Theory

Abstract

The theory of surfaces has undergone substantial changes in recent years, with many different active areas at this point in time. It has become mainstream to study minimal surfaces and constant mean curvature surfaces in more general target spaces than space forms. So far, the main strands of development center around methods from the theory of elliptic differential equations, complex analytic methods, and integrable systems techniques. The study of singular surfaces has widened the classical point of view and seems to be a particularly promising direction of research when considering certain moduli space problems.