References
[BdC1] Barbosa, J.L., Carmo, M. do: On the size of minimal surface inR 3. Am. J. Math.98(2), 515–528 (1976)
[BdC2] Barbosa, J.L., Carmo, M. do: Stability of minimal surfaces and eigenvalues of the Laplacian. Math. Z.173, 13–28 (1980)
[BdC3] Barbosa, J.L., Carmo, M. do: Stability of hypersurfaces with constant mean curvature. Math. Z.185, 339–353 (1984)
[BdCE] Barbosa, J.L., Carmo, M. do, Eschenburg, J.: Stability of hypersurfaces of constant mean curvature in Riemannian manifolds. Preprint
[BM] Barbosa, J.L., Mori, H.: Stability of constante mean curvature surfaces in Riemannian 3-space form. Yokohama Math. J.30, 72–79 (1982)
[Br] Bryant, R.L.: Surfaces of mean curvature one in hyperbolic space. Preprint
[CY] Cheng, S.Y., Yau, S.T.: Differential equations on Riemannian manifolds and their geometric applications. Comm. Pure Appl. Math.28, 333–354 (1975)
[dCD] Carmo, M. do, Dajczer, M.: Rotations hypersurfaces in spaces of constant curvature. Trans. AMS227(2), 685–709 (1983)
[dCP] Carmo, M. do, Peng, C.K.: Stable complete minimal surfaces in ℝ3 are planes. Bull. Am. Math. Soc. (NS)1, 903–906 (1979)
[F-C] Fischer Colbrie, D.: On complete minimal surfaces with finite Morse index in 3-manifolds. Invent. math.82, 121–132 (1985)
[F-C, S] Fischer Colbrie, D., Schoen, R.: The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature. Comm. Pure Appl. Math.35, 199–211 (1980)
[Go] Gomes, J.M.: Sobre hipersuperficies com curvatura média constante no espaço hiperbólico. Tese de Doutorado (IMPA), 1984
[GRR] Gomes J.M., Rippol, J.B., Rodríguez, L.: On surfaces of constant mean curvature in hyperbolic space. Preprint
[GL] Gulliver, R., Lawson, H.B.: The structure of stable minimal hypersurfaces near a singularity. Am. Math. Soc. Proc. Symp. Pure Math.44, 207–237 (1986)
[Hu] Huber, A.: On subharmonic functions and differential geometry in the large. Comm. Math. Helv.32, 13–72 (1957)
[S] Smale, S.: On the Morse index theorem. J. Math. Mech.14, 1049–1056 (1965)
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da Silveira, A.M. Stability of complete noncompact surfaces with constant mean curvature. Math. Ann. 277, 629–638 (1987). https://doi.org/10.1007/BF01457862
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DOI: https://doi.org/10.1007/BF01457862