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Erschienen in:
1987 | OriginalPaper | Buchkapitel
Immersed Tori of Constant Mean Curvature in R 3
verfasst von : Henry C. Wente
Erschienen in: Variational Methods for Free Surface Interfaces
Verlag: Springer New York
Enthalten in: Professional Book Archive
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In this chapter we show how to construct immersions of tori into Euclidean space R3 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].