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].
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© 1987 Springer-Verlag New York Inc.
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Wente, H.C. (1987). Immersed Tori of Constant Mean Curvature in R 3 . In: Concus, P., Finn, R. (eds) Variational Methods for Free Surface Interfaces. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4656-5_2
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DOI: https://doi.org/10.1007/978-1-4612-4656-5_2
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