Skip to main content
SpringerLink
Log in

Measures on spaces of surfaces

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

Function spaces, pseudodifferential operators, and partial differential equations

  1. Robert A. Adams, Sobolev Spaces, Academic Press, NY, 1975.

    Google Scholar 

  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.

  3. Lars Hörmander, Linear Partial Differential Operators, Springer-Verlag, NY, 1976.

    Google Scholar 

  4. Lars Hörmander, The spectral function of an elliptic operator, Acta Mathematica 121 (1968), 193–218.

    MATH  MathSciNet  Google Scholar 

  5. Olga A. Ladyzhenskaya & Nina N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, NY, 1968.

    Google Scholar 

  6. C. B. Morrey, Jr., Multiple Integrals in the Calculus of Variations, Springer-Verlag, NY, 1966.

    Google Scholar 

  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].)

  8. R. T. Seeley, Refinement of the functional calculus of Calderon and Zygmund, Kon. Ned. Ak. van Wet. 68 (1965), 521–531.

    MATH  MathSciNet  Google Scholar 

  9. R. T. Seeley, The resolvent of an elliptic boundary problem, Am. J. Math. 91 (1969), 889–919.

    MATH  MathSciNet  Google Scholar 

  10. R. T. Seeley, Topics in pseudo-differential operators, Pseudo-differential Operators, C. I. M. E., Rome, 1969, 169–305.

    Google Scholar 

  11. Elias M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970.

    Google Scholar 

Geometry

  1. William K. Allard, On the first variation of a varifold: boundary behavior, Ann. of Math. 101 (1975), 418–446.

    MATH  MathSciNet  Google Scholar 

  2. 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. Herbert Federer, Geometric Measure Theory, Springer-Verlag, NY, 1969.

    Google Scholar 

  4. 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.

    MATH  MathSciNet  Google Scholar 

  5. Victor Guillemin & Alan Pollack, Differential Topology, Prentice-Hall, Englewood Cliffs, NJ, 1974.

    Google Scholar 

  6. Frank Morgan, Almost every curve in R3 bounds a unique area minimizing surface, Inventiones Math. 45 (1978), 253–297.

    Article  ADS  MATH  Google Scholar 

  7. Frank Morgan, A smooth curve in R4 bounding a continuum of area minimizing surfaces, Duke Math. J. 43 (1976), 867–870.

    Article  MATH  MathSciNet  Google Scholar 

  8. Robert Osserman, Minimal Varieties, Bull. Amer. Math. Soc. 75 (1969), 1092–1120.

    MATH  MathSciNet  Google Scholar 

Probability and measure theory

  1. Jens Peter Reus Christensen, On sets of Haar measure zero in abelian Polish groups, Israel J. Math. 13 (1972), 255–260.

    MathSciNet  Google Scholar 

  2. Jean Delporte, Fonctions aléatoires presque sûrement continues sur un intervalle fermé, Ann. Inst. Henri Poincaré (Sec. B) 1 (1964), 111–215.

    MATH  MathSciNet  Google Scholar 

  3. J. L. Doob, Stochastic Processes, Wiley, NY, 1967.

    Google Scholar 

  4. R. M. Dudley, Non-existence of quasi-invariant measures on infinite-dimensional locally compact convex spaces. Mimeographed notes.

  5. Paul R. Halmos, Measure Theory, van Nostrand, NY, 1950.

    Google Scholar 

  6. G. A. Hunt, Random Fourier transforms, Trans. Amer. Math. Soc. 71 (1951), 38–69.

    MATH  MathSciNet  Google Scholar 

  7. Kiyosi Itô & Henry P. McKean, Jr., Diffusion Processes and their Sample Paths, Springer-Verlag, NY, 1965.

    Google Scholar 

  8. Shizuo Kakutani, On equivalence of infinite product measures, Ann. of Math. (2) 49 (1948), 214–224.

    MATH  MathSciNet  Google Scholar 

  9. Hui-Hsiung Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Math. 463, Springer-Verlag, NY, 1975.

  10. Laurent Schwartz, Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Oxford University Press, NY, 1973.

    Google Scholar 

  11. Laurent Schwartz, Cylindrical probabilities and p-summing and p-Radonifying maps, Seminar Schwanz, Pirie Printers Pty. Limited, Canberra, 1977.

    Google Scholar 

  12. V. N. Sudakov, Linear sets with quasi-invariant measure (in Russian), Doklady Akademii Nauk. SSSR 127 (1959), 524–525.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts

    Frank Morgan

Authors
  1. Frank Morgan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by G. Strang

Rights and permissions

Reprints and permissions

About this article

Cite this article

Morgan, F. Measures on spaces of surfaces. Arch. Rational Mech. Anal. 78, 335–359 (1982). https://doi.org/10.1007/BF00249585

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00249585

Keywords

Search

Navigation