Some remarks on elliptic equations and infinitesimal deformations of submanifolds

  • Vladimir Oliker
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 838)


Fundamental Form Normal Bundle Deformation Field Elementary Symmetric Function Rigidity Result 
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  1. [1]
    A.D. Aleksandrov, Uniqueness theorems for surfaces in the large, I, Vestnik Leningrad Univ. 11, no. 19 (1956), 5–17; English translation, Amer. Math. Soc. Transl. Ser. 2, 21 (1962), 341–416.MathSciNetzbMATHGoogle Scholar
  2. [2]
    S.Y. Cheng and S.T. Yau, On the regularity of the solution of n-dimensional Minkowski problem, Comm. Pure Appl. Math. 29 (1976), 495–516.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    D. Hilbert, Grundzüge einer Allgemeinen Theorie der Linearen Integralgleichungen, Kap. XIX, Leipzig und Berlin, 1912.Google Scholar
  4. [4]
    Y. Mutō, Deformability of a submanifold in Euclidean space whose image by the Gauss map is fixed, Proceedings of the AMS, 76, no. 1 (1979), 140–144.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    V.I. Oliker, Eigenvalues of the Laplacian and uniqueness in the Minkowski problem. J. Differential Geometry, v. 14, no. 1 (1979).Google Scholar
  6. [6]
    _____, Infinitesimal deformations preserving parallel normal vector fields, Proceedings of the Conference on Geometry, Haifa, Israel, 1979. Lecture Notes in Math., Springer-V. V. 192Google Scholar
  7. [7]
    A.V. Pogorelov, Multidimensional Minkowski Problem, New York, J. Wiley, 1978.zbMATHGoogle Scholar
  8. [8]
    Yu. A. Volkov and V.I. Oliker, Uniqueness of the solution of Christoffel’s problem for nonclosed surfaces (Russian), Mat. Zametki, 8, no. 2 (1970), 251–257; English translation, Math. Notes of the Academy of Sciences of the USSR, 8, nos. 1–2 (1970), 611–614.MathSciNetGoogle Scholar
  9. [9]
    K. Yano, Infinitesimal variations of submanifolds, Kodai Math. J., 1 (1978), 30–44.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    v. I. Oliker: On compact submanifolds with nondegenerate parallel normal vector fields. Pacific. J. Math., to appear.Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Vladimir Oliker
    • 1
  1. 1.University of IowaIowa CityU.S.A.

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