Some remarks on deformations of minimal surfaces
Authors: Harold Rosenberg and Éric Toubiana
Journal: Trans. Amer. Math. Soc. 295 (1986), 491-499
MSC: Primary 53A10
MathSciNet review: 833693
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.
-  William 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, https://doi.org/10.1007/BF02588319
-  Harold Rosenberg, Deformations of complete minimal surfaces, Trans. Amer. Math. Soc. 295 (1986), no. 2, 475–489. MR 833692, https://doi.org/10.1090/S0002-9947-1986-0833692-0
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