On differentiability of minimal surfaces at a boundary point
HTML articles powered by AMS MathViewer
- by Tunc Geveci PDF
- 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 $P$.References
- David Kinderlehrer, The boundary regularity of minimal surfaces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 23 (1969), 711–744. MR 262943
- Johannes C. C. Nitsche, The boundary behavior of minimal surfaces. Kellogg’s theorem and Branch points on the boundary, Invent. Math. 8 (1969), 313–333. MR 259766, DOI 10.1007/BF01404636
- S. E. Warschawski, Boundary derivatives of minimal surfaces, Arch. Rational Mech. Anal. 38 (1970), 241–256. MR 262944, DOI 10.1007/BF00281522
- S. E. Warschawski, On differentiability at the boundary in conformal mapping, Proc. Amer. Math. Soc. 12 (1961), 614–620. MR 131524, DOI 10.1090/S0002-9939-1961-0131524-8
- Stefan E. Warschawski, On the higher derivatives at the boundary in conformal mapping, Trans. Amer. Math. Soc. 38 (1935), no. 2, 310–340. MR 1501813, DOI 10.1090/S0002-9947-1935-1501813-X
Additional Information
- © Copyright 1971 American Mathematical Society
- 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