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Transactions of the American Mathematical Society

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Deformations of complete minimal surfaces


Author: Harold Rosenberg
Journal: Trans. Amer. Math. Soc. 295 (1986), 475-489
MSC: Primary 53A10
MathSciNet review: 833692
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Abstract: A notion of deformation is defined and studied for complete minimal surfaces in $ {R^3}$ and $ {R^3}/G,G$ a group of translations. The catenoid, Enneper's surface, and the surface of Meeks-Jorge, modelled on a $ 3$-punctured sphere, are shown to be isolated. Minimal surfaces of total curvature $ 4\pi $ in $ {R^3}/Z$ and $ {R^3}/{Z^2}$ are studied. It is proved that the helicoid and Scherk's surface are isolated under periodic perturbations.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9947-1986-0833692-0
Article copyright: © Copyright 1986 American Mathematical Society