A note on diastatic entropy and balanced metrics

Abstract

We give un upper bound Ent(Ω, g)<λ of the diastatic entropy Ent(Ω, g) of a complex bounded domain (Ω, g) in terms of the balanced condition (in Donaldson terminology) of the Kaehler metric λg. When (Ω, g) is a homogeneous bounded domain we show that the converse holds true, namely if Ent(Ω, g)<1 then g is balanced. Moreover, we explcit compute Ent(Ω, g) in terms of Piatetski-Shapiro constants.

7 pages

References in corpus (4)

• Berezin quantization of homogeneous bounded domains
• A bounded homogeneous domain and a projective manifold are not relatives
• The volume entropy of local Hermitian symmetric space of noncompact type
• Upper and lower bounds for the first eigenvalue and the volume entropy of noncompact Kähler manifolds

Cited by in corpus (5)

• Some remarks on homogeneous Kähler manifolds
• Bochner coordinates on flag manifolds
• On the diastatic entropy and C^1-rigidity of complex hyperbolic manifolds
• Upper and lower bounds for the first eigenvalue and the volume entropy of noncompact Kähler manifolds
• A Cartan-Hartogs version of the Polydisk Theorem