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Li, Peter

On the Sobolev constant and the p-spectrum of a compact Riemannian manifold. (English) Zbl 0466.53023

Ann. Sci. Éc. Norm. Supér. (4) 13, 451-468 (1980).
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Cited in 2 Reviews
Cited in 86 Documents

MSC:

53C20 Global Riemannian geometry, including pinching
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)

Keywords:

Sobolev constant; isoperimetric constant; Laplacian on forms; eigenvalues and multiplicities; Ricci curvature

Citations:

Zbl 0465.53032
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\textit{P. Li}, Ann. Sci. Éc. Norm. Supér. (4) 13, 451--468 (1980; Zbl 0466.53023)
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References:

[1] E. BOMBIERI , Theory of Minimal Surfaces and a Counter-Example to the Bernstein Conjecture in High Dimension (Lecture Notes, Courant Institute, 1970 ).
[2] J. CHEEGER , A Lower Bound for the Smallest Eigenvalue of the Laplacian in Problem in Analysis , a Symposium in honor of S. Bochner, Princeton University Press, Princeton, 1970 . Zbl 0212.44903 · Zbl 0212.44903
[3] S. Y. CHENG , Eigenfunctions and Nodal Sets (Comment Math. Helv., Vol. 51, 1976 , pp. 43-55). MR 53 #1661 | Zbl 0334.35022 · Zbl 0334.35022
[4] C. CROKE , Some Isoperimetric Inequalities and Consequences (Ann. scient. Éc. Norm. Sup., (4), T. 13, 1980 , pp. 419-435). Numdam | MR 83d:58068 | Zbl 0465.53032 · Zbl 0465.53032
[5] S. GALLOT and D. MEYER , Operateur de courbure et laplacien des formes différentielles d’une variété riemannienne (J. Math. pures et appl., Vol. 54, 1975 , pp. 259-284). MR 56 #13128 | Zbl 0316.53036 · Zbl 0316.53036
[6] M. GROMOV , Manifolds of Negative Curvature (preprint). · Zbl 0433.53028
[7] R. OSSERMAN , The Isoperimetric Inequality (Bulletin A.M.S., Vol. 84, No. 6, 1978 , pp. 1182-1238). Article | MR 58 #18161 | Zbl 0411.52006 · Zbl 0411.52006
[8] S. T. YAU , Isoperimetric Constants and the First Eigenvalue of a Compact Riemannian Manifold (Ann. scient. Éc. Norm. Sup., Vol. 4, t. 8, 1975 , pp. 487-507). Numdam | MR 53 #1478 | Zbl 0325.53039 · Zbl 0325.53039
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