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arXiv · 1303.3217

A note on diastatic entropy and balanced metrics

Roberto Mossa
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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.

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Roberto Mossa. 2014-10-19. A note on diastatic entropy and balanced metrics. https://doi.org/10.1016/j.geomphys.2014.10.004

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