Skip to main content
Log in

The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature

  • 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

  • [A] Allard, W.K.: On the first variation of a varifold. Ann. Math.95, 417–491 (1972)

    Google Scholar 

  • [AA] Allard, W.K., Almgren, Jr., F.J.: On the radial behavior of minimal surfaces and the uniqueness of their tangent cones. Ann. Math.113, 215–265 (1981)

    Google Scholar 

  • [An] Anderson, M.: Curvature estimates for minimal surfaces in 3-manifold. Preprint

  • [B] Bryant, R.: Conformal and minimal immersions of compact surfaces into the 4-sphere. J. Diff. Geom.17, 455–474 (1982)

    Google Scholar 

  • [CW] Choi, H.I., Wang, A.N.: A first eigenvalue estimate for minimal hypersurfaces. J. Diff. Geom.18, 559–562 (1983)

    Google Scholar 

  • [F] Frankel, T.: On the fundamental group of a compact minimal submanifold. Ann. Math.83, 68–73 (1966)

    Google Scholar 

  • [G1] Gulliver, R.: Regularity of minimizing surfaces of prescribed mean curvature. Ann. Math.97, 275–305 (1973)

    Google Scholar 

  • [G2] Gulliver, R.: Removability of singular points on surfaces of bounded mean curvature. J. Diff. Geom.11, 345–350 (1976)

    Google Scholar 

  • [HKW] Hildebrandt, S., Kaul, H., Widman, K.-O.: An existence theorem for harmonic mappings of Riemannian manifolds. Acta Math.138, 1–16 (1977)

    Google Scholar 

  • [M] Morrey, C.B.: Multiple integrals in the calculus of variations. Berlin-Heidelberg-New York: Springer 1969

    Google Scholar 

  • [MY] Meek, III, W.H., Yau, S.T.: The classical Plateua problem and the topology of three-dimensional manifolds. Topology21, 409–442 (1982)

    Google Scholar 

  • [O] Otsuki, T.: Minimal hypersurfaces in a Riemannian manifold of constant curvature. Amer. J. Math.92, 145–173 (1970)

    Google Scholar 

  • [S] Sampson, J.H.: Some properties and applications of harmonic mappings. Ann. Sci. Ec. Norm. Sup11, 211–228 (1978)

    Google Scholar 

  • [SS] Schoen, R., Simon, L.: Regularity of simply connected surfaces with quasiconformal Gauss map. Ann. Math. Stud. Vol. 103, pp. 127–145. Princeton University Press (1983)

    Google Scholar 

  • [SSY] Schoen, R., Simon, L., Yau, S.T.: Curvature estimates for minimal hypersurfaces. Acta Math.134, 275–288 (1975)

    Google Scholar 

  • [SU] Sacks, J., Uhlenbeck, K.: The existence of minimal immersions of 2-spheres. Ann. Math.113 1–24 (1981)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research of both authors partially supported by NSF Grants

Rights and permissions

Reprints and permissions

About this article

Cite this article

Choi, H.I., Schoen, R. The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature. Invent Math 81, 387–394 (1985). https://doi.org/10.1007/BF01388577

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388577

Keywords

Navigation