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

2012/11/12 by Roberto Mossa, Mossa, Roberto
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Spectral Theory (math.SP) #math.CV #math.DG #math.SP

paper · pdf · doi:10.48550/arxiv.1211.2705

13 pages

openalex publication_date 2012/11/12 · arxiv created 2015/02/02 · arxiv updated 2015/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the isoperimetric constant of symmetric spaces of noncompact type

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