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A brief survey of some recent developments in spectral geometry

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1207)

Keywords

  • Riemannian Manifold
  • Riemann Surface
  • Heat Kernel
  • Direct Problem
  • Closed Geodesic

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General references

  1. BERARD, P.-BERGER, M.-Le Spectre d'une variété riemannienne en 1982, in Spectra of Riemannian Manifolds, Kaigai Publications 1983, p. 139–194 (see Appendix B).

    Google Scholar 

  2. BANDLE, C.-Isoperimetric inequalities and applications, Pitman 1980.

    Google Scholar 

  3. BERGER, M.-GAUDUCHON, P.-MAZET, E.-Le spectre d'une variété riemannienne, Lecture Notes in Mathematics no 194, Springer 1971.

    Google Scholar 

  4. BERENSTEIN, C.-Autovalores del Laplaciano y geometria, VII ELAM, Fondo Editorial, acta cientifica venezolana, Caracas 1984.

    MATH  Google Scholar 

  5. CHAVEL, I.-Eigenvalues in Riemannian Geometry, Academic Press 1984.

    Google Scholar 

  6. BERARD, P.-A propos de "Eigenvalues in Riemannian Geometry" de I. Chavel, Gazette des Mathématiciens, Soc. Math. France 1986 to appear.

    Google Scholar 

  7. GUILLEMIN, V.-Lectures on spectral theory of elliptic operators, Duke Math. J. 44 (1977), 485–517.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. GUILLEMIN, V.-Some classical theorems in spectral theory revisited, in Seminar on singularities of solutions of partial differential equations, ed. by L. Hörmander, Annals of Math. Studies no 91, Princeton Univ. Press 1979.

    Google Scholar 

  9. GUILLEMIN, V.-STERNBERG, S.-Geometric asymptotics, Amer. Math. Soc. 1977.

    Google Scholar 

  10. GILKEY, P.B.-The index theorem and the heat equation, Publish or Perish Inc, 1974.

    Google Scholar 

  11. PAYNE, L.E.-Isoperimetric inequalities and their applications, SIAM Review 9 (1967), 453–488.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. POLYA, G.-SZEGO, G.-Isoperimetric inequalities in mathematical physics, Annals of Math. Studies 27, Princeton University Press 1951.

    Google Scholar 

  13. OSSERMAN, R.-The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), 1182–1238.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1986 Springer-Verlag

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Bérard, P.H. (1986). A brief survey of some recent developments in spectral geometry. In: Spectral Geometry: Direct and Inverse Problems. Lecture Notes in Mathematics, vol 1207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076337

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  • DOI: https://doi.org/10.1007/BFb0076337

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16788-4

  • Online ISBN: 978-3-540-40958-8

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