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Inventiones mathematicae

, Volume 88, Issue 2, pp 243–256 | Cite as

Curvature estimates and compactness theorems in 3-manifolds for surfaces that are stationary for parametric elliptic functionals

  • B. White
Article

Keywords

Compactness Theorem Curvature Estimate Elliptic Functional Parametric Elliptic Functional 
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] Anderson, M.: Curvature estimates and compactness theorems for minimal surfaces in 3-manifolds. Ann. Sci. Ec. Norm. Super., IV. Ser.18, 89–105 (1985)Google Scholar
  2. [ASS] Almgren, F.J., Jr., Schoen, R., Simon, L.: Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals. Acta Math139, 217–265 (1977)Google Scholar
  3. [CS] Choi, H., 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)Google Scholar
  4. [GT] Gilbarg, D., Trudinger, N.: Elliptic partial differential equations of second order (2nd edition). Berlin-Heidelberg-New York: Springer 1983Google Scholar
  5. [HS] Hardt, R., Simon, L.: Boundary regularity and embedded solutions for the oriented plateau problem. Ann. Math.110, 439–486 (1979)Google Scholar
  6. [O] Osserman, R.: Global properties of minimal surfaces inE 3 andE n. Ann. Math.80, 340–364 (1964)Google Scholar
  7. [S] Simon, L.: Remarks on curvature estimates for minimal hypersurfaces. Duke Math. J.43, 545–553 (1976)Google Scholar
  8. [SS1] Schoen, R., Simon, L.: Regularity of stable minimal hypersurfaces. Commun. Pure Appl. Math.34, 741–797 (1981)Google Scholar
  9. [SS2] Schoen, R., Simon, L.: Regularity of stmply connected surfaces with quasiconformal gauss map, in Seminar on minimal submanifolds. Ann. Math. Stud.103, 127–145 (1983)Google Scholar
  10. [W1] White, B.: The space ofk-dimensional surfaces that are stationary with respect to a parametric elliptic functional. Indiana Univ. Math. J. (in press) (1987)Google Scholar
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • B. White
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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