Advertisement

The heat equation and geometry for the \(\bar \partial\)-Neumann problem

  • Richard Beals
  • Nancy K. Stanton
Special Year Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 1276)

Keywords

Asymptotic Expansion Heat Equation Heat Kernel Pseudodifferential Operator Real Hypersurface 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. 1.
    R. Beals, P.C. Greiner, and N.K. Stanton, The heat equation on a CR manifold, J. Differential Geometry, 20 (1984), 343–387.MathSciNetzbMATHGoogle Scholar
  2. 2.
    R. Beals and N.K. Stanton, The heat equation for the \(\bar \partial\)-Neumann problem, I, preprint.Google Scholar
  3. 3.
    R. Beals and N.K. Stanton, The heat equation for the \(\bar \partial\)-Neumann problem, II, preprint.Google Scholar
  4. 4.
    J. Brüning and E. Heintze, The asymptotic expansion of Minakshisundaram-Pleijel in the equivariant case, Duke Math. J. 51 (1984), 959–980.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    J. Brüning and R. Seeley, Regular Singular Asymptotics, Advances in Math. 58 (1985), 133–148.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    C.J. Callias and G.A. Uhlmann, Singular asymptotic approach to partial differential equations with isolated singularities in the coefficients, Bull. A.M.S. 11 (1984), 172–176.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    J. Cheeger, Spectral geometry of singular Riemannian spaces, J. Differential Geometry 18 (1983), 575–657.MathSciNetzbMATHGoogle Scholar
  8. 8.
    P.C. Greiner, An asymptotic expansion for the heat equation, Arch. Rational Mech. Anal. 41 (1971), 163–218.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    P.C. Greiner and E.M. Stein, Estimates for the \(\bar \partial\)-Neumann Problem, Math. Notes 19, Princeton Univ. Press, Princeton, N.J., 1977.zbMATHGoogle Scholar
  10. 10.
    H.P. McKean, Jr., and I.M. Singer, Curvature and the eigenvalues of the Laplacian, J. Differential Geometry 1 (1967), 43–69.MathSciNetzbMATHGoogle Scholar
  11. 11.
    G. Métivier, Spectral asymptotics of the \(\bar \partial\)-Neumann Duke problem, Duke Math. J. 48 (1981), 779–806.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    R. Seeley, Analytic extension of the trace associated with elliptic boundary value problems, Amer. J. Math. 91 (1969), 963–983.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    C.M. Stanton, Intrinsic connections for Levi metrics, in preparation.Google Scholar
  14. 14.
    S.M. Webster, Pseudo-hermitian structures on a real hypersurface, J. Differential Geometry 13 (1978), 25–41.MathSciNetzbMATHGoogle Scholar
  15. 15.
    H. Weyl, Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung), Math. Ann. 71 (1912), 441–479.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Richard Beals
    • 1
  • Nancy K. Stanton
    • 2
  1. 1.Department of MathematicsYale UniversityNew Haven
  2. 2.Department of MathematicsUniversity of Notre DameNotre Dame

Personalised recommendations