Geometry of Surfaces, Soliton Equations and Loop Groups

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9705479 Dorfmeister This project lies in the area of minimal surfaces and harmonic mappings. Earlier, the investigator has developed a Weierstrass type formula for harmonic maps from Riemann surfaces into compact symmetric spaces. The current project is a continuation of that work. In particular, the method is to be applied to produce constant mean curvature surfaces in 3-space. Minimal surfaces and constant mean curvature surfaces have certain optimizing properties; as a consequence, they have important physical applications. For example, the interface of two homogeneous media often forms a minimal surface as such a surface tends to be locally energy-minimizing. Constant mean curvature surfaces arise as closed surfaces that have the least surface area amongst all closed surfaces enclosing a fixed volume.