Abstract
In [JW] the disk-type minimal surfaces spanning a given Jordan curve Γ in a Riemannian manifold N is studied. In 1948, C.B. Morrey [M] proved that there exists at least one solution to this problem. In fact he proved the existence of the surface of least area among the surfaces with boundary Γ. An interesting question is whether there are other minimal surfaces with the same boundary besides. When the ambient space N is the standard n-sphere S n, M.Ji and G.Y. Wang contributes a neat result: Conclusion A. Each smooth Jordan curve Γ in S n bounds at least two minimal surfaces, sometimes infinitely many ones.
Supported by Foundation of Academia Sinica and NNSF of China
1991 Mathematics Subject Classification: 58E12, 49Q05, 53A10, 53C42
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Wang, G. (1994). Minimal Surfaces in Riemannian Manifolds. In: Gu, C., Ding, X., Yang, CC. (eds) Partial Differential Equations in China. Mathematics and Its Applications, vol 288. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1198-0_8
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DOI: https://doi.org/10.1007/978-94-011-1198-0_8
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