do Carmo, Manfredo Perdigão; Peng, C. K. Stable complete minimal surfaces in \(R^3\) are planes. (English) Zbl 0442.53013 Bull. Am. Math. Soc., New Ser. 1, 903-906 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 ReviewsCited in 101 Documents MSC: 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 49Q05 Minimal surfaces and optimization 49Q20 Variational problems in a geometric measure-theoretic setting Keywords:minimal surfaces; stable; Laplacian; Gaussian curvature; conformal Citations:Zbl 0442.53012; Zbl 0439.53060 PDF BibTeX XML Cite \textit{M. P. do Carmo} and \textit{C. K. Peng}, Bull. Am. Math. Soc., New Ser. 1, 903--906 (1979; Zbl 0442.53013) Full Text: DOI OpenURL References: [1] J. L. Barbosa and M. do Carmo, On the size of a stable minimal surface in \?³, Amer. J. Math. 98 (1976), no. 2, 515 – 528. · Zbl 0332.53006 [2] M. do Carmo and A. M. da Silveira, Globally stable complete minimal surfaces in R, Proc. Amer. Math. Soc. (to appear). · Zbl 0442.53011 [3] M. do Carmo and C. K. Peng, Stable complete minimal hypersurfaces, Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations, Vol. 1, 2, 3 (Beijing, 1980) Sci. Press Beijing, Beijing, 1982, pp. 1349 – 1358. [4] Doris Fischer-Colbrie and Richard Schoen, The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature, Comm. Pure Appl. Math. 33 (1980), no. 2, 199 – 211. · Zbl 0439.53060 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.