Recent Developments in the Theory of Minimal Surfaces

In this article we describe recent (within the past 4 or 5 years) results in minimal surface theory, with particular emphasis on the existence and regularity theory. For a more general survey, including some technical background discussion and a more comprehensive bibliography, the reader is referred to [30]. Throughout the article «?f will denote ÄJ-dimensional Hausdorff measure (in Euclidean space or in a general Eiemannian manifold) and J5^(|) (often denoted simply JBe(£)) will denote the ball in R n with radius Q > 0 and centre f. For convenience we break our discussion into several sections, although naturally there is some overlap between these.