The Global Theory of Minimal Surfaces in Flat Spaces [electronic resource] : Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Martina Franca, Italy July 7-14, 1999 / by William H. Meeks III, Antonio Ros, Harold Rosenberg.

William H. Meeks III: Minimal Surfaces in Flat Three Dimensional Spaces -- Joaquin Perez, Antonio Ros: Properly embedded minimal surfaces with finite total curvature -- Harold Rosenberg: Bryant Surfaces.

In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry and surfaces of constant mean curvature in the hyperbolic space.