Lower bound estimates of the first eigenvalue for compact manifolds with positive Ricci curvature

Pacific Journal of Mathematics

Volumn 190, Issue 2, 1999, Pages 383-398

  Yang, DaGang ^a  

^a TULANE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040626313     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.1999.190.383     Document Type: Article

References (11)

1. J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, Problems in Analysis, a symposium in honor of S. Bochner, Princeton Univ. Press, Princeton, 1970.
2. J. Escobar, Uniqueness theorems on conformal deformation of metrics, Sobolev inequalities, and an eigenvalue estimate.
3. P. Li, A lower bound for the first eigenvalue of the Laplacian on a compact Riemannian manifold, Indiana Univ. Math. J., 28 (1979), 1013-1019.
4. _, Lecture Notes on Geometric Analysis, Lecture Notes Series, #6, Seoul National University, Seoul, Korea.
5. P. Li and S.T. Yau, Eigenvalues of a compact Riemannian manifold, AMS Proc. Symp. Pure Math., 36 (1980), 205-239.
6. A. Lichnerowicz, Géometrie des groupes de transformations, Dunod, Paris, 1958.
7. M. Obata, Certain conditions for a Riemannian manifold to be isometric to the sphere, J. Math. Soc. Japan, 14 (1962), 333-340.
8. R. Reilly, Applications of the Hessian operator in a Riemannian manifold, Indiana Univ. Math. J., 26 (1977), 459-472.
9. R. Schoen and S.T. Yau, Lectures on Differential Geometry, Conference Proceedings and Lecture Notes in Geometry and Topology, Vol. I, International Press, 1994.
10. S.T. Yau, Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold, Ann. Scient. Éc. Norm. Sup., 4 (1985), 487-507.
11. H.C. Yang and J.Q. Zhong, On the estimate of the first eigenvalue of a compact Riemannian manifold, Sci. Sinica Ser., A27 (1984), 1265-1273.