Immersed Tori of Constant Mean Curvature in R 3

Henry C. Wente

A chapter in Variational Methods for Free Surface Interfaces, 1987, pp 13-26 from Springer

Abstract: Abstract In this chapter we show how to construct immersions of tori into Euclidean space R 3 which have constant mean curvature H ≠ 0. We thus exhibit an example of a “non-round” soap bubble (although it does self-intersect) providing a counterexample to a conjecture attributed to H. Hopf. We shall carefully 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].

Keywords: Fundamental Domain; Round Sphere; Soap Bubble; Umbilic Point; Complex Analytic Function (search for similar items in EconPapers)
Date: 1987
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:978-1-4612-4656-5_2

Ordering information: This item can be ordered from
http://www.springer.com/9781461246565

DOI: 10.1007/978-1-4612-4656-5_2

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 ().