Upper and lower bounds for the first eigenvalue and the volume entropy of noncompact K\"ahler manifolds

Roberto Mossa

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arXiv · 1211.2705

Upper and lower bounds for the first eigenvalue and the volume entropy of noncompact K\"ahler manifolds

Roberto Mossa

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Abstract

We find upper and lower bounds for the first eigenvalue and the volume entropy of a noncompact real analytic K\"ahler manifold, in terms of Calabi's diastasis function and diastatic entropy, which are sharp in the case of the complex hyperbolic space. As a corollary we obtain explicit lower bounds for the first eigenvalue of the geodesic balls of an Hermitian symmetric space of noncompact type.

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Roberto Mossa. 2012-11-12. Upper and lower bounds for the first eigenvalue and the volume entropy of noncompact K\"ahler manifolds. https://arxiv.org/abs/1211.2705

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