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

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1276)

Keywords

  • Asymptotic Expansion
  • Heat Equation
  • Heat Kernel
  • Pseudodifferential Operator
  • Real Hypersurface

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Bibliography

  1. R. Beals, P.C. Greiner, and N.K. Stanton, The heat equation on a CR manifold, J. Differential Geometry, 20 (1984), 343–387.

    MathSciNet  MATH  Google Scholar 

  2. R. Beals and N.K. Stanton, The heat equation for the \(\bar \partial\)-Neumann problem, I, preprint.

    Google Scholar 

  3. R. Beals and N.K. Stanton, The heat equation for the \(\bar \partial\)-Neumann problem, II, preprint.

    Google Scholar 

  4. J. Brüning and E. Heintze, The asymptotic expansion of Minakshisundaram-Pleijel in the equivariant case, Duke Math. J. 51 (1984), 959–980.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. J. Brüning and R. Seeley, Regular Singular Asymptotics, Advances in Math. 58 (1985), 133–148.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. J. Cheeger, Spectral geometry of singular Riemannian spaces, J. Differential Geometry 18 (1983), 575–657.

    MathSciNet  MATH  Google Scholar 

  8. P.C. Greiner, An asymptotic expansion for the heat equation, Arch. Rational Mech. Anal. 41 (1971), 163–218.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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.

    MATH  Google Scholar 

  10. H.P. McKean, Jr., and I.M. Singer, Curvature and the eigenvalues of the Laplacian, J. Differential Geometry 1 (1967), 43–69.

    MathSciNet  MATH  Google Scholar 

  11. G. Métivier, Spectral asymptotics of the \(\bar \partial\)-Neumann Duke problem, Duke Math. J. 48 (1981), 779–806.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. R. Seeley, Analytic extension of the trace associated with elliptic boundary value problems, Amer. J. Math. 91 (1969), 963–983.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. C.M. Stanton, Intrinsic connections for Levi metrics, in preparation.

    Google Scholar 

  14. S.M. Webster, Pseudo-hermitian structures on a real hypersurface, J. Differential Geometry 13 (1978), 25–41.

    MathSciNet  MATH  Google Scholar 

  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1987 Springer-Verlag

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Beals, R., Stanton, N.K. (1987). The heat equation and geometry for the \(\bar \partial\)-Neumann problem. In: Berenstein, C.A. (eds) Complex Analysis II. Lecture Notes in Mathematics, vol 1276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078951

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  • DOI: https://doi.org/10.1007/BFb0078951

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18357-0

  • Online ISBN: 978-3-540-47904-8

  • eBook Packages: Springer Book Archive