On differentiability of minimal surfaces at a boundary point

Geveci, Tunc

doi:10.1090/S0002-9939-1971-0273523-8

On differentiability of minimal surfaces at a boundary point
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Proc. Amer. Math. Soc. 28 (1971), 213-218 Request permission

Abstract:

Let $F(z) = \{ u(z),v(z),w(z)\} ,|z| < 1$, 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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