Minimal Surfaces with Free Boundaries and Unstable Minimal Surfaces

Richard Courant
Additional contact information
Richard Courant: New York University, Institute for Mathematics and Mechanics

Chapter Chapter VI in Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces, 1950, pp 199-243 from Springer

Abstract: 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.

Keywords: Harmonic Function; Unit Circle; Free Boundary; Minimal Surface; Jordan Curve (search for similar items in EconPapers)
Date: 1950
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-9917-2_7

Ordering information: This item can be ordered from
http://www.springer.com/9781461299172

DOI: 10.1007/978-1-4612-9917-2_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().