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The uniqueness for minimal surfaces in \(S^ 3\). (English) Zbl 0667.49025

Author’s abstract: “We give a sufficient condition on a Jordan curve \(\Gamma\) in the 3-dimensional open hemisphere H of \(S^ 3\) in terms of the Hopf fibering under which \(\Gamma\) spans a unique compact generalized minimal surface in H. The maximum principle for minimal surfaces in \(S^ 3\) is provided and plays an important role in the proof of the uniqueness theorem.”
Reviewer: C.Udrişte

MSC:

49Q05 Minimal surfaces and optimization
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
58E12 Variational problems concerning minimal surfaces (problems in two independent variables)
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References:

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