Some remarks on deformations of minimal surfaces
Harold Rosenberg and Éric Toubiana
Trans. Amer. Math. Soc. 295 (1986), 491-499
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Abstract: We consider complete minimal surfaces (c.m.s.'s) in and their deformations. is an -deformation of if is a graph over in an tubular neighborhood of and is -close to . A minimal surface is isolated if all c.m.s.'s which are sufficiently small deformations of are congruent to .
In this paper we construct an example of a nonisolated c.m.s. It is modelled on a -punctured sphere and is of finite total curvature. On the other hand, we prove that a c.m.s. discovered by Meeks and Jorge, modelled on the sphere punctured at the fourth roots of unity, is isolated.
H. Meeks III, A survey of the geometric results in the classical
theory of minimal surfaces, Bol. Soc. Brasil. Mat. 12
(1981), no. 1, 29–86. MR 671473
Rosenberg, Deformations of complete minimal
surfaces, Trans. Amer. Math. Soc.
295 (1986), no. 2,
833692 (88a:53005a), http://dx.doi.org/10.1090/S0002-9947-1986-0833692-0
- W. Meeks, A survey of the geometric results in the classical theory of minimal surfaces, Bol. Soc. Brasil. Mat. 12 (1981), 29-86. MR 671473 (84d:53007)
- H. Rosenberg, Deformations of complete minimal surfaces, Trans. Amer. Math. Soc. 295 (1986), 475-489. MR 833692 (88a:53005a)
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