Upper and lower bounds for the first eigenvalue and the volume entropy of noncompact Kähler manifolds

Abstract

We find upper and lower bounds for the first eigenvalue and the volume entropy of a noncompact real analytic Kähler 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.

13 pages

References in corpus (2)

• A note on diastatic entropy and balanced metrics
• On the isoperimetric constant of symmetric spaces of noncompact type

Cited by in corpus (1)

• A note on diastatic entropy and balanced metrics