Inventiones mathematicae

, Volume 81, Issue 3, pp 387–394 | Cite as

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

  • Hyeong In Choi
  • Richard Schoen
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References

  1. [A] Allard, W.K.: On the first variation of a varifold. Ann. Math.95, 417–491 (1972)Google Scholar
  2. [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
  3. [An] Anderson, M.: Curvature estimates for minimal surfaces in 3-manifold. PreprintGoogle Scholar
  4. [B] Bryant, R.: Conformal and minimal immersions of compact surfaces into the 4-sphere. J. Diff. Geom.17, 455–474 (1982)Google Scholar
  5. [CW] Choi, H.I., Wang, A.N.: A first eigenvalue estimate for minimal hypersurfaces. J. Diff. Geom.18, 559–562 (1983)Google Scholar
  6. [F] Frankel, T.: On the fundamental group of a compact minimal submanifold. Ann. Math.83, 68–73 (1966)Google Scholar
  7. [G1] Gulliver, R.: Regularity of minimizing surfaces of prescribed mean curvature. Ann. Math.97, 275–305 (1973)Google Scholar
  8. [G2] Gulliver, R.: Removability of singular points on surfaces of bounded mean curvature. J. Diff. Geom.11, 345–350 (1976)Google Scholar
  9. [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
  10. [M] Morrey, C.B.: Multiple integrals in the calculus of variations. Berlin-Heidelberg-New York: Springer 1969Google Scholar
  11. [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
  12. [O] Otsuki, T.: Minimal hypersurfaces in a Riemannian manifold of constant curvature. Amer. J. Math.92, 145–173 (1970)Google Scholar
  13. [S] Sampson, J.H.: Some properties and applications of harmonic mappings. Ann. Sci. Ec. Norm. Sup11, 211–228 (1978)Google Scholar
  14. [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
  15. [SSY] Schoen, R., Simon, L., Yau, S.T.: Curvature estimates for minimal hypersurfaces. Acta Math.134, 275–288 (1975)Google Scholar
  16. [SU] Sacks, J., Uhlenbeck, K.: The existence of minimal immersions of 2-spheres. Ann. Math.113 1–24 (1981)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Hyeong In Choi
    • 1
  • Richard Schoen
    • 2
  1. 1.University of ChicagoChicagoUSA
  2. 2.University of CaliforniaBerkeleyUSA

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