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arXiv · 2006.07061

Finite entropy vs finite energy

Eleonora Di Nezza·Vincent Guedj·Chinh H. Lu
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Abstract

Probability measures with either finite Monge-Amp\`ere energy or finite entropy have played a central role in recent developments in K\"ahler geometry. In this note we make a systematic study of quasi-plurisubharmonic potentials whose Monge-Amp\`ere measures have finite entropy. We show that these potentials belong to the finite energy class ${\mathcal E}^{\frac{n}{n-1}}$, where $n$ denotes the complex dimension, and provide examples showing that this critical exponent is sharp. Our proof relies on refined Moser-Trudinger inequalities for quasi-plurisubharmonic functions.

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Eleonora Di Nezza, Vincent Guedj, Chinh H. Lu. 2020-06-12. Finite entropy vs finite energy. https://arxiv.org/abs/2006.07061

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