A note on Riesz potentials and the first eigenvalue
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- by Jie Cheng Chen PDF
- Proc. Amer. Math. Soc. 117 (1993), 683-685 Request permission
Abstract:
In this paper, we consider the boundedness of Riesz potentials on positively curved manifolds. As an application, we get the greatest lower bound of the essential spectrum of a positively curved manifold.References
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J.-Ch. Chen, Heat kernels on positively curved manifolds, Ph.D. Thesis, Hangzhou Univ., 1987.
- Jie Cheng Chen and Jia Yu Li, A note on eigenvalues, Chinese Sci. Bull. 35 (1990), no. 7, 536–540. MR 1056801
- Harold Donnelly, On the essential spectrum of a complete Riemannian manifold, Topology 20 (1981), no. 1, 1–14. MR 592568, DOI 10.1016/0040-9383(81)90012-4
- José F. Escobar, On the spectrum of the Laplacian on complete Riemannian manifolds, Comm. Partial Differential Equations 11 (1986), no. 1, 63–85. MR 814547, DOI 10.1080/03605308608820418
- H. P. McKean, An upper bound to the spectrum of $\Delta$ on a manifold of negative curvature, J. Differential Geometry 4 (1970), 359–366. MR 266100
- Noël Lohoué, Puissances complexes de l’opérateur de Laplace-Beltrami, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 13, A605–A608 (French, with English summary). MR 572646
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
- Robert S. Strichartz, Analysis of the Laplacian on the complete Riemannian manifold, J. Functional Analysis 52 (1983), no. 1, 48–79. MR 705991, DOI 10.1016/0022-1236(83)90090-3 R. Schoen and S. T. Yau, Differential geometry, Chinese Academic Press, 1988. (Chinese)
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 683-685
- MSC: Primary 58G11; Secondary 35P15, 46E35, 58G25
- DOI: https://doi.org/10.1090/S0002-9939-1993-1110540-4
- MathSciNet review: 1110540