Archive for Rational Mechanics and Analysis

, Volume 78, Issue 4, pp 335–359 | Cite as

Measures on spaces of surfaces

  • Frank Morgan


Neural Network Complex System Nonlinear Dynamics Electromagnetism 
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Function spaces, pseudodifferential operators, and partial differential equations

  1. 1.
    Robert A. Adams, Sobolev Spaces, Academic Press, NY, 1975.Google Scholar
  2. 2.
    A. P. Calderon, Lebesgue spaces of differentiable functions and distributions, Proceedings of Symposia in Pure Mathematics, Vol. IV, Partial Differential Equations, Amer. Math. Soc. 1961, 33–49.Google Scholar
  3. 3.
    Lars Hörmander, Linear Partial Differential Operators, Springer-Verlag, NY, 1976.Google Scholar
  4. 4.
    Lars Hörmander, The spectral function of an elliptic operator, Acta Mathematica 121 (1968), 193–218.zbMATHMathSciNetGoogle Scholar
  5. 5.
    Olga A. Ladyzhenskaya & Nina N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, NY, 1968.Google Scholar
  6. 6.
    C. B. Morrey, Jr., Multiple Integrals in the Calculus of Variations, Springer-Verlag, NY, 1966.Google Scholar
  7. 7.
    R. T. Seeley, Complex powers of an elliptic operator, Proceedings of Symposia in Pure Math., Vol. X, Pseudodifferential Operators, Amer. Math. Soc., 1967, 288–307. (Corrections to some inconsequential errors in the proofs appear in [9].)Google Scholar
  8. 8.
    R. T. Seeley, Refinement of the functional calculus of Calderon and Zygmund, Kon. Ned. Ak. van Wet. 68 (1965), 521–531.zbMATHMathSciNetGoogle Scholar
  9. 9.
    R. T. Seeley, The resolvent of an elliptic boundary problem, Am. J. Math. 91 (1969), 889–919.zbMATHMathSciNetGoogle Scholar
  10. 10.
    R. T. Seeley, Topics in pseudo-differential operators, Pseudo-differential Operators, C. I. M. E., Rome, 1969, 169–305.Google Scholar
  11. 11.
    Elias M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970.Google Scholar


  1. 12.
    William K. Allard, On the first variation of a varifold: boundary behavior, Ann. of Math. 101 (1975), 418–446.zbMATHMathSciNetGoogle Scholar
  2. 13.
    Frederick J. Almgren, Mass minimizing integral currents in R nare almost everywhere regular, Preliminary report, Notices Amer. Math. Soc. 24 (1977), A-541.Google Scholar
  3. 14.
    Herbert Federer, Geometric Measure Theory, Springer-Verlag, NY, 1969.Google Scholar
  4. 15.
    Herbert Federer, The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension, Bull. Amer. Math. Soc. 76 (1970), 767–771.zbMATHMathSciNetGoogle Scholar
  5. 16.
    Victor Guillemin & Alan Pollack, Differential Topology, Prentice-Hall, Englewood Cliffs, NJ, 1974.Google Scholar
  6. 17.
    Frank Morgan, Almost every curve in R3 bounds a unique area minimizing surface, Inventiones Math. 45 (1978), 253–297.CrossRefADSzbMATHGoogle Scholar
  7. 18.
    Frank Morgan, A smooth curve in R4 bounding a continuum of area minimizing surfaces, Duke Math. J. 43 (1976), 867–870.CrossRefzbMATHMathSciNetGoogle Scholar
  8. 19.
    Robert Osserman, Minimal Varieties, Bull. Amer. Math. Soc. 75 (1969), 1092–1120.zbMATHMathSciNetGoogle Scholar

Probability and measure theory

  1. 20.
    Jens Peter Reus Christensen, On sets of Haar measure zero in abelian Polish groups, Israel J. Math. 13 (1972), 255–260.MathSciNetGoogle Scholar
  2. 21.
    Jean Delporte, Fonctions aléatoires presque sûrement continues sur un intervalle fermé, Ann. Inst. Henri Poincaré (Sec. B) 1 (1964), 111–215.zbMATHMathSciNetGoogle Scholar
  3. 22.
    J. L. Doob, Stochastic Processes, Wiley, NY, 1967.Google Scholar
  4. 23.
    R. M. Dudley, Non-existence of quasi-invariant measures on infinite-dimensional locally compact convex spaces. Mimeographed notes.Google Scholar
  5. 24.
    Paul R. Halmos, Measure Theory, van Nostrand, NY, 1950.Google Scholar
  6. 25.
    G. A. Hunt, Random Fourier transforms, Trans. Amer. Math. Soc. 71 (1951), 38–69.zbMATHMathSciNetGoogle Scholar
  7. 26.
    Kiyosi Itô & Henry P. McKean, Jr., Diffusion Processes and their Sample Paths, Springer-Verlag, NY, 1965.Google Scholar
  8. 27.
    Shizuo Kakutani, On equivalence of infinite product measures, Ann. of Math. (2) 49 (1948), 214–224.zbMATHMathSciNetGoogle Scholar
  9. 28.
    Hui-Hsiung Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Math. 463, Springer-Verlag, NY, 1975.Google Scholar
  10. 29.
    Laurent Schwartz, Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Oxford University Press, NY, 1973.Google Scholar
  11. 30.
    Laurent Schwartz, Cylindrical probabilities and p-summing and p-Radonifying maps, Seminar Schwanz, Pirie Printers Pty. Limited, Canberra, 1977.Google Scholar
  12. 31.
    V. N. Sudakov, Linear sets with quasi-invariant measure (in Russian), Doklady Akademii Nauk. SSSR 127 (1959), 524–525.zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag GmbH & Co. KG 1981

Authors and Affiliations

  • Frank Morgan
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridge

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