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Some bounds for eigenvalues of the Laplace operator acting on forms on a compact Riemannian manifold are derived.In case of manifolds without boundary we give upper bounds in terms of the curvature, its covariant derivative and the injectivity radius.For a small geodesic ball upper and lower bounds of eigenvalues in terms of bounds of sectional curvature are given.
Józef Dodziuk (Mon,) studied this question.