Skip to main content
Log in

New surfaces of constant mean curvature

  • 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.

Institutional subscriptions

References

  • [doC] Do Carmo, M.: Differential geometry of curves and surfaces. New Jersey: Prentice Hall 1976

    MATH  Google Scholar 

  • [D] Delaunay, C.: Sur la surface de révolution, dont la courbure moyenne est constante. J. Math.6 (1841)

  • [DHKW] Dierkes, U., Hildebrandt, S., Küster, A., Wohlrab, O.: Minimal surfaces I. Berlin Heidelberg New York: Springer 1992

    MATH  Google Scholar 

  • [G] Gulliver, R.: Regularity of minimizing surfaces of prescribed mean curvature. Ann. Math.97, 275–305 (1973)

    Article  MathSciNet  Google Scholar 

  • [GL] Gulliver, R., Lesley, F.D.: On boundary branch points of minimizing surfaces. Arch. Ration. Mech. Anal.52, 20–25 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  • [H1] Hildebrandt, S.: Boundary behaviour of minimal surfaces. Arch. Ration. Mech. Anal.35, 47–82 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  • [H2] Hildebrandt, S.: Maximum principles for minimal surfaces and for surfaces of constant mean curvature. Math. Z.128, 253–259 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  • [Kpl] Kapouleas, N.: Complete constant mean curvature surfaces in Euclidean three-space. Ann. Math.131, 239–330 (1990)

    Article  MathSciNet  Google Scholar 

  • [Kp2] Kapouleas, N.: Compact constant mean curvature surfaces in Euclidean three-space. J. Differ. Geom.33, 683–715 (1991)

    MATH  MathSciNet  Google Scholar 

  • [Ka] Karcher, H.: The triply periodic minimal surfaces of A. Schoen and their constant mean curvature companions. Manuscr. Math.64, 291–357 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  • [KKS] Korevaar, N., Kusner, R., Solomon, B.: The structure of complete embedded surfaces with constant mean curvature. J. Differ. Geom.30, 465–503 (1989)

    MATH  MathSciNet  Google Scholar 

  • [L] Lawson, H.B.: Complete minimal surfaces in S3. Ann. Math.92, 335–374 (1970)

    Article  MathSciNet  Google Scholar 

  • [MY] Meeks, W.H., Yau, S.T.: The existence of embedded minimal surfaces and the problem of uniqueness. Math. Z.179, 131–168 (1982)

    Article  MathSciNet  Google Scholar 

  • [O] Osserman, R.: A proof of regularity everywhere of the classical solution to Plateau's problem. Ann. Math.91, 1092–1120 (1969)

    Google Scholar 

  • [PS] Pinkall, U., Sterling, I.: On the classification of constant mean curvature tori. Ann. Math.130, 407–451 (1989)

    Article  MathSciNet  Google Scholar 

  • [S] Schoen, R.: Estimates for stable minimal surfaces in three dimensional manifolds. In: Bombieri, E. (ed.) Seminar on Minimal Submanifolds. (Ann. Math. Stud., vol. 103, pp. 111–126) Princeton: Princeton University Press 1983

    Google Scholar 

  • [We] Wente, H.: Constant mean curvature immersions of Enneper type. Memoirs of the AMS, vol. 478, 1992

  • [Wh] White, B.: Curvature estimates and compactness theorems in 3-manifolds for surfaces that are stationary for parametric elliptic functionals. Invent. Math.88, 243–256 (1987)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Große-Brauckmann, K. New surfaces of constant mean curvature. Math Z 214, 527–565 (1993). https://doi.org/10.1007/BF02572424

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02572424

Keywords

Navigation