Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite entropy vs finite energy   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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The categories of this paper are: stat
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga