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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
Article

Keywords

Manifold Ricci Curvature Positive Ricci Curvature Minimal Embedding 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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