Abstract
In this chapter we will prove that the only simple closed surfaces with constant mean curvature H are the spheres. From this theorem and the main theorem of the preceding chapter it follows that the only undecided cases are non-simple closed surfaces with genus > O.
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© 1983 Springer-Verlag Berlin Heidelberg
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Hopf, H. (1983). Simple Closed Surfaces (of Arbitrary Genus) with Constant Mean Curvature — Generalizations. In: Differential Geometry in the Large. Lecture Notes in Mathematics, vol 1000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21563-0_12
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DOI: https://doi.org/10.1007/978-3-662-21563-0_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12004-9
Online ISBN: 978-3-662-21563-0
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