Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces

An examination of approaches to easy-to-understand but difficult-to-solve mathematical problems, this classic text balances the individuality of objects with the generality of mathematical methods. Beginning with a discussion of Dirichlet's principle and the boundary value problem of potential theory, the text proceeds to examinations of conformal mapping on parallel-slit domains and Plateau's problem. Succeeding chapters explore the general problem of Douglas and conformal mapping of multiply connected domains, concluding with a survey of minimal surfaces with free boundaries and unstable minimal surfaces. 1950 ed.