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The uniqueness for minimal surfaces inS 3

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Abstract

We give a sufficient condition on a Jordan curve Γ in the 3-dimensional open hemisphereH ofS 3 in terms of the Hopf fibering under which Γ spans a unique compact generalized minimal surface inH. The maximum principle for minimal surfaces inS 3 is proved and plays an important role in the proof of the uniqueness theorem.

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Authors and Affiliations

  1. Department of Mathematics, Osaka University, Toyonaka, 560, Osaka, Japan

    Miyuki Koiso

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  1. Miyuki Koiso
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Dedicated to Professor Shingo Murakami on his 60th birthday

This work was carried out while the author was a visitor to the Max-Planck-Institut für Mathematik.

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Koiso, M. The uniqueness for minimal surfaces inS 3 . Manuscripta Math 63, 193–207 (1989). https://doi.org/10.1007/BF01168871

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  • DOI: https://doi.org/10.1007/BF01168871

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