Skip to main content
SpringerLink
Log in

Boundary derivatives of minimal surfaces

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliography

  1. Goluzin, G.M., Geometric Theory of Functions of a Complex Variable. Translation from 2nd Russian ed.; Vol. 26, Transl. of Math. Monographs, A.M.S. 1969.

  2. Heinz, E., & Tomi, F., Zu einem Satz von S. Hildebrandt über das Randverhalten von Minimalflächen. Mathem. Zeitschrift 111, 372–386 (1969).

    Google Scholar 

  3. Hildebrandt, S., Boundary behavior of minimal surfaces. Arch. Rational Mech. Anal. 35, 47–82 (1969).

    Google Scholar 

  4. Lesley, F.D., Differentiability of minimal surfaces at the boundary (to appear).

  5. Lewy, H., On the boundary behavior of minimal surfaces. Proceed Nat. Acad. Sci., U.S.A. 37, 103–111 (1951).

    Google Scholar 

  6. Nitsche, Johannes C.C., On new results in the theory of minimal surfaces. Bulletin Amer. Math. Society 71, 195–270 (1965).

    Google Scholar 

  7. Nitsche, Johannes C.C., The boundary behavior of minimal surfaces. Kellogg's theorem and branch points on the boundary. Inventiones Mathematicae 8, 313–333 (1969).

    Google Scholar 

  8. Privalov, I.I., Randeigenschaften analytischer Funktionen (Translation). Berlin: VEB Deutscher Verlag der Wissenschaften 1956.

    Google Scholar 

  9. Riesz, F. & M., Über die Randwerte einer analytischen Function. Compte rendu du quatrième congrès des math. scand. à Stockholm, 27–44 (1916).

  10. Tsuji, M., On a theorem of F. and M. Riesz. Proc. Imp. Acad. Tokyo 18, 172–175 (1942).

    Google Scholar 

  11. Warschawski, S.E., Über einige Konvergenzsätze aus der Theorie der konformen Abbildung. Nachrichten von der Gesellschaft der Wiss. Göttingen, Math.-Phys. Klasse, 1930, 344–369.

  12. Warschawski, S.E., On the higher derivatives at the boundary in conformal mapping. Transactions, Amer. Math. Soc. 38, 310–340 (1935).

    Google Scholar 

  13. Warschawski, S.E., On differentiability at the boundary in conformal mapping. Proceeding, Amer. Math. Soc. 12, 614–620 (1961).

    Google Scholar 

  14. Zygmund, A., Trigonometric Series, 2nd ed., Vol. 1 (1959), Cambridge University Press.

  15. Kinderlehrer, D., Boundary regularity of minimal surfaces, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 23, 711–747 (1969) [added in proof].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, San Diego, La Jolla

    S. E. Warschawski

Authors
  1. S. E. Warschawski
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by J. C. C. Nitsche

This research was supported (in part) by U.S. Air Force Grant AFOSR-68-1514.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Warschawski, S.E. Boundary derivatives of minimal surfaces. Arch. Rational Mech. Anal. 38, 241–256 (1970). https://doi.org/10.1007/BF00281522

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00281522

Keywords

Search

Navigation