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Minimal Surfaces with Free Boundaries and Unstable Minimal Surfaces

In: Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces

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  • Richard Courant

    (New York University, Institute for Mathematics and Mechanics)

Abstract

In this chapter we shall discuss two extensions of the theory of minimal surfaces. First we shall solve the problem of finding minimal surfaces of least area when the whole boundary or part of it is not prescribed but left free on given manifolds.1 Secondly we shall study minimal surfaces whose areas are not relative minima. Minimal surfaces of this type correspond to unstable equilibria of a soap film; they will therefore he referred to as unstable minimal surfaces.

Suggested Citation

  • Richard Courant, 1950. "Minimal Surfaces with Free Boundaries and Unstable Minimal Surfaces," Springer Books, in: Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces, chapter 0, pages 199-243, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-9917-2_7
    DOI: 10.1007/978-1-4612-9917-2_7
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