Bounds for Laplace eigenvalues of Kaehler metrics

Abstract

We prove inequalities for Laplace eigenvalues of Kaehler manifolds generalising to higher eigenvalues the classical inequality for the first Laplace eigenvalue due to Bourguignon, Li, and Yau in 1994. We also obtain similar inequalities for analytic varieties in Kaehler manifolds.

17 pages, final version; inaccuracies and typos corrected, minor stylistic changes

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