Skip to main content
Log in

Über Flächen konstanter mittlerer Krümmung

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

Literatur

  1. Beckert, H.: Existenzbeweise mehrdimensionaler regulärer Variationsprobleme. Math. Ann.133, 191–218 (1957).

    Google Scholar 

  2. Bernstein, S.: Sur les surfaces définies au moyen de leur courbure moyenne ou totale. Ann. École Norm. Sup.27, 233–256 (1910).

    Google Scholar 

  3. Courant, R.: On a generalized form of Plateau's problem. Trans. Amer. Math. Soc.50, 40–47 (1941).

    Google Scholar 

  4. —: Dirichlet's principle, conformal mapping and minimal surfaces. New York: Interscience Publ. 1950.

    Google Scholar 

  5. Heinz, E.: Über die Existenz einer Fläche konstanter mittlerer Krümmung bei vorgegebener Berandung. Math. Ann.127, 258–287 (1954).

    Google Scholar 

  6. —: An inequality of isoperimetric type for surfaces of constant mean curvature. Arch. Rat. Mech. Analysis33, 155–168 (1969).

    Google Scholar 

  7. Heinz, E.: Unstable surfaces of constant mean curvature. Arch. Rat. Mech. Analysis. (Erscheint demnächst.)

  8. Hildebrandt, S.: Über das Randverhalten von Minimalflächen. Math. Ann.165, 1–18 (1966).

    Google Scholar 

  9. —: Über Minimalflächen mit freiem Rand. Math. Z.95, 1–19 (1967).

    Google Scholar 

  10. Hildebrandt, S.: Boundary behavior of minimal surfaces. To appear in: Arch. Rat. Mech. Analysis (1969).

  11. Hildebrandt, S., Heinz, E.: On the number of branch points of surfaces of bounded mean curvature. Journal of Differential Geometry (erscheint demnächst).

  12. Hildebrandt, S.: Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie. (Erscheint demnächst.)

  13. Lewy, H.: On the boundary behavior of minimal surfaces. Proc. Nat. Acad. Sci. USA37, 103–110 (1951).

    Google Scholar 

  14. —: On minimal surfaces with partially free boundary. Commun. Pure Appl. Math.4, 1–13 (1951).

    Google Scholar 

  15. Morrey, C. B.: On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc.43, 126–166 (1938).

    Google Scholar 

  16. — Multiple integral problems in the calculus of variations and related topics. Univ. California Publ. Math., New Ser.,1, No. 1, 1–130 (1943).

    Google Scholar 

  17. —: The problem of Plateau on a Riemannian manifold. Ann. of Math.49, 807–851 (1949).

    Google Scholar 

  18. —: Multiple integrals in the calculus of variations. Berlin-Heidelberg-New York: Springer 1966.

    Google Scholar 

  19. Nirenberg, L.: Remarks on strongly elliptic partial differential equations. Commun. Pure Appl. Math.8, 648–674 (1955).

    Google Scholar 

  20. —: On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa, Ser. 3,13, 115–162 (1959).

    Google Scholar 

  21. Warschawski, S.: On the differentiability at the boundary in conformal mapping. Proc. Amer. Math. Soc.12, 614–620 (1961).

    Google Scholar 

  22. Werner, H.: Das Problem von Douglas für Flächen konstanter mittlerer Krümmung. Math. Ann.133, 303–319 (1957).

    Google Scholar 

  23. — The existence of surfaces of constant mean curvature with arbitrary Jordan curves as assigned boundary. Proc. Amer. Math. Soc.11, 63–70 (1960).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Die Untersuchungen dieser Arbeit wurden zum Teil am Courant Institute of Mathematical Sciences, New York University, durchgeführt und dabei von der National Science Foundation, Grant NSF-GP-8724, unterstützt.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hildebrandt, S. Über Flächen konstanter mittlerer Krümmung. Math Z 112, 107–144 (1969). https://doi.org/10.1007/BF01115036

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01115036

Navigation