Kobayashi, Shoshichi 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]. Reviewer: Klaus Kirsten (Manchester) MSC: 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions Keywords:first eigenvalue estimates; Laplacian PDFBibTeX XMLCite \textit{S. Kobayashi}, in: 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; Zbl 1009.58020)