Minimal surfaces in 𝑆^{𝑚} with Gauss curvature ≤0

Minimal surfaces in $S^{m}$ with Gauss curvature $\leq 0$
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Proc. Amer. Math. Soc. 31 (1972), 235-238

DOI: https://doi.org/10.1090/S0002-9939-1972-0286000-6

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Closed minimal surfaces in a unit $m$-sphere ${S^m}$ with Gauss curvature $K \leqq 0$ are considered.

References

Bang-yen Chen, Minimal hypersurfaces in an $m$-sphere, Proc. Amer. Math. Soc. 29 (1971), 375–380. MR 285999, DOI 10.1090/S0002-9939-1971-0285999-0
S. S. Chern, M. do Carmo, and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968) Springer, New York, 1970, pp. 59–75. MR 0273546

Minimal varieties in constant curvature manifolds

H. Blaine Lawson Jr., Complete minimal surfaces in $S^{3}$, Ann. of Math. (2) 92 (1970), 335–374. MR 270280, DOI 10.2307/1970625
H. Blaine Lawson Jr., The global behavior of minimal surfaces in $S^{n}$, Ann. of Math. (2) 92 (1970), 224–237. MR 270279, DOI 10.2307/1970835