## Stable complete minimal surfaces in $$R^3$$ are planes.(English)Zbl 0442.53013

### 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
Full Text:

### 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
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