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On first eigenvalues of the Laplacian. (English) Zbl 1009.58020

Nagano, Tadashi (ed.) et al., Proceedings of the workshop on geometry and its applications in honor of Morio Obata, Yokohama, Japan, November 19-21, 1991. Singapore: World Scientific. 101-107 (1993).
This contribution summarizes some results on the first eigenvalue of the Laplacian on compact Riemannian manifolds and compact Kähler manifolds with metric \(g\). Under the assumption that the Ricci tensor \(\rho\geq cg\), \(c> 0\), an upper limit for the first eigenvalue is given.
For the entire collection see [Zbl 0981.00018].

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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