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Eigenvalue comparison theorems and its geometric applications

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References

  1. Berger, M., Gauduchon, P., Mazet, E.: Le spectre d'une variété Riemannienne. Lecture Notes in Mathematics 194. Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  2. Bishop, R., Crittenden, R.: Geometry of Manifolds. New York-London: Academic Press 1964

    Google Scholar 

  3. Chavel, I., Feldman, E.: The first eigenvalue of the Laplacian on manifolds of non-negative curvature. CUNY preprint

  4. Cheeger, J.: The relation between the Laplacian and the diameter for manifolds of non-negative curvature. Arch. der Math.19, 558–560 (1968)

    Google Scholar 

  5. Cheng, S. Y.: Eigenvalue and eigenfunctions of the Laplacian. To appear in the Proceedings of the Symposium on Differential Geometry. (Stanford University, 1973)

  6. Hobson, E.W.: Spherical and Ellipsoidal Harmonics. New York: Chelsea 1955

    Google Scholar 

  7. Klingenberg, W.: Contribution to Riemannian geometry in the large. Ann. of Math., II. Ser.69, 654–666 (1959)

    Google Scholar 

  8. Mazet, E.: Une majoration de λ1 du type de Cheeger. C.r. Acad. Sci., Paris, Sér. A,277, 171–174 (1973)

    Google Scholar 

  9. McKean, H.P. Jr.: An upper bound to the spectrum on a manifold of negative curvature. J. diff. Geometry4, 359–366 (1970)

    Google Scholar 

  10. Payne, L.E.: Isoperimetric inequalities and their applications. SIAM Review9, 453–488 (1967)

    Google Scholar 

  11. Watson, G.N.: A treatise on the theory of Bessel functions. Cambridge: Cambridge University Press 1944; New York: MacMillan 1944

    Google Scholar 

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Cheng, SY. Eigenvalue comparison theorems and its geometric applications. Math Z 143, 289–297 (1975). https://doi.org/10.1007/BF01214381

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