Skip to main content
Log in

The Plateau problem for surfaces of prescribed mean curvature in a cylinder

  • Published:
Inventiones mathematicae Aims and scope

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.

References

  1. Courant, R.: Dirichlet's principle, conformal mapping, and minimal surfaces. New York: Interscience 1950.

    Google Scholar 

  2. Gulliver, R.: On regularity of generalized surfaces of constant mean curvature. Bull A.M.S.77, 243–246 (1971).

    Google Scholar 

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

    Google Scholar 

  4. Hildebrandt, S.: Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritästheorie I. Math. Z.112, 205–213 (1969).

    Google Scholar 

  5. — On the Plateau problem for surfaces of constant mean curvature. Comm. Pure Appl. Math.23, 97–114 (1970).

    Google Scholar 

  6. Serrin, J.: Or the Dirichlet problem for surfaces of constant mean curvature (to appear).

  7. Tomi, F.: Ein einfacher Beweis eines Regularitätssatzes für schwache Lösungen gewisser elliptischer Systeme. Math. Z.112, 214–218 (1969).

    Google Scholar 

  8. Wente, H.: An existence theorem for surfaces of constant mean curvature. J. Math. Anal. Appl.26, 318–344 (1969).

    Google Scholar 

  9. Heinz, E.: On the nonexistence of a surface of constant mean curvature with finite area and prescribed rectifiable boundary. Arch. Rational Mech. Anal.35, 249–250 (1969).

    Google Scholar 

  10. Hildebrandt, S.: Über einen neuen Existenzsatz für Flächen vorgeschriebener mittlerer Krümmung (preprint).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gulliver, R., Spruck, J. The Plateau problem for surfaces of prescribed mean curvature in a cylinder. Invent Math 13, 169–178 (1971). https://doi.org/10.1007/BF01390099

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01390099

Keywords

Navigation