Globally stable complete minimal surfaces in 𝑅³

do Carmo, M.; Da Silveira, A. M.

doi:10.1090/S0002-9939-1980-0565370-X

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Globally stable complete minimal surfaces in $\textbf {R}^{3}$
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by M. do Carmo and A. M. Da Silveira

Proc. Amer. Math. Soc. 79 (1980), 345-346

DOI: https://doi.org/10.1090/S0002-9939-1980-0565370-X

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Abstract:

It is proved that a globally stable complete minimal surface in ${R^3}$ with finite total curvature is a plane.

References

J. L. Barbosa and M. do Carmo, On the size of a stable minimal surface in $R^{3}$, Amer. J. Math. 98 (1976), no. 2, 515–528. MR 413172, DOI 10.2307/2373899
Robert Osserman, Global properties of minimal surfaces in $E^{3}$ and $E^{n}$, Ann. of Math. (2) 80 (1964), 340–364. MR 179701, DOI 10.2307/1970396
Jaak Peetre, A generalization of Courant’s nodal domain theorem, Math. Scand. 5 (1957), 15–20. MR 92917, DOI 10.7146/math.scand.a-10484