Titlebook: Variational Methods for Free Surface Interfaces; Proceedings of a Con Paul Concus,Robert Finn Conference proceedings 1987 Springer-Verlag N

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Stability of a Drop Trapped Between Two Parallel Planes: Preliminary Report,sted of omitting most proofs. I have been informed by Professor Stephan Hildebrandt that his student, Maria Athanassenas, has independently derived the stability results for contact angles equal to π/2, apparently using different methods.

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Immersed Tori of Constant Mean Curvature in ,,, state the theorems involved in the construction and also provide a geometric description (with suggestive sketches) of the desired surfaces. An expanded version complete with proofs appeared in a recent paper of the author [11].

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Interfaces of Prescribed Mean Curvature,enting in a sense a simplified physical situation, and investigate some basic properties of its solutions. The results we obtain may serve both as an illustration of the use of certain variational techniques and as an instance of results that could be obtained, under appropriate conditions, in more general cases.

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,Convexity Properties of Solutions to Elliptic P.D.E.’S, this note we shall study some particular estimates involving ., ., ...: ones that are related to convexity properties of .. The results do not usually lead to existence theorems (with some exceptions, e.g. [3]), but are surprising and have independent beauty.

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The Construction of Families of Embedded Minimal Surfaces,with William H. Meeks III. Our research made critical use of the graphics programming software developed by James T. Hoffman at the University of Massachusetts. The central theorem is the following existence result [4], [5], [6].