Minimal Surfaces I (eBook, PDF)
Boundary Value Problems
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Vol. 1 provides an introduction to the classical theory of minimal surfaces in three-dimensional Euclidean space as well as a presentation of basic results on boundary value problems for minimal surfaces. Existence results are emphasized, but uniqueness and nonuniqueness questions, isoperimetric inequalities, geometric inclusion theorems and related topics are also dealt with. Surveys of important discoveries of the last 20 years lead the reader to the frontiers of present research. Vol. 2 presents a comprehensive study of the boundary behaviour of minimal surfaces. This is a fascinating part ...
Vol. 1 provides an introduction to the classical theory of minimal surfaces in three-dimensional Euclidean space as well as a presentation of basic results on boundary value problems for minimal surfaces. Existence results are emphasized, but uniqueness and nonuniqueness questions, isoperimetric inequalities, geometric inclusion theorems and related topics are also dealt with. Surveys of important discoveries of the last 20 years lead the reader to the frontiers of present research. Vol. 2 presents a comprehensive study of the boundary behaviour of minimal surfaces. This is a fascinating part of the regularity theory for solutions of nonlinear elliptic boundary problems for systems of elliptic systems of partial differential equations.
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