论文标题
有限熵与有限能量
Finite entropy vs finite energy
论文作者
论文摘要
有限的monge-ampère能量或有限熵的概率度量在Kähler几何形状的最新发展中起着核心作用。在本说明中，我们对蒙格 - 安am措施具有有限熵的准毛刺势进行了系统的研究。我们表明，这些电位属于有限的能量类$ {\ Mathcal E}^{\ frac {n} {n} {n-1}} $，其中$ n $表示复杂的维度，并提供了示例，表明此关键指数很清晰。我们的证明依赖于精制的Moser-trudinger不平等现象来实现准毛发功能。
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.
