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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On differentiability of minimal surfaces at a boundary point


Author: Tunc Geveci
Journal: Proc. Amer. Math. Soc. 28 (1971), 213-218
MSC: Primary 53.04
DOI: https://doi.org/10.1090/S0002-9939-1971-0273523-8
MathSciNet review: 0273523
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Abstract: Let $ F(z) = \{ u(z),v(z),w(z)\} ,\vert z\vert < 1$, represent a minimal surface spanning the curve $ \Gamma :\{ U(s),V(s),W(s)\} ,s$ being the arc length. Suppose $ \Gamma $ has a tangent at a point $ P$. Then $ F(z)$ is differentiable at this point if $ U'(s),V'(s),W'(s)$ satisfy a Dini condition at $ P$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0273523-8
Keywords: Complex analysis, minimal surfaces, boundary behavior
Article copyright: © Copyright 1971 American Mathematical Society