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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,Boundary Behavior of Nonparametric Minimal Surfaces—Some Theorems and Conjectures,ept possibly at (0,0), where it might have a jump discontinuity. Then for all directions from (0,0) into ., the radial limits of . exist, where . is the solution of the minimal surface equation in . or of an equation of prescribed (bounded) mean curvature in . with . and .. Some conjectures which would generalize this result are mentioned.

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On the Existence of Embedded Minimal Surfaces of Higher Genus with Free Boundaries in Riemannian MaIn this chapter we consider the following configuration: a Riemannian manifold . of bounded geometry, some closed Jordan curves Γ., and a supporting surface ∂., disjoint from the Γ.. We further assume that the Γ. are contained in a suitable barrier ∂. of nonnegative mean curvature (cf. §2 for details).

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A Mathematical Description of Equilibrium Surfaces,The central point in many problems of mathematical physics is answering questions about the boundary of a region, using as little information as possible about the region itself.

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