有限熵与有限能量
Finite entropy vs finite energy
摘要：
概率测度无论是有限的蒙赫-安培能量或有限的熵发挥了核心作用，在最近的发展凯勒几何。本文系统地研究了Monge-Ampère测度具有有限熵的拟多重次调和势。我们表明，这些潜力属于有限能量类${\mathcal E}^{\frac{n}{n-1}}$，其中$n$表示复杂的尺寸，并提供的例子表明，这个临界指数是尖锐的。我们的证明依赖于拟多重次调和函数的精化Moser-Trudinger不等式。
英文摘要：
Probability measures with either finite Monge-Ampère energy or finite entropy have played a central role in recent developments in Kähler geometry. In this note we make a systematic study of quasi-plurisubharmonic potentials whose Monge-Ampère 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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