Lelong数的精确球-固体均值公式及消失准则
An Exact Spherical-Solid Mean Formula and Vanishing Criteria for Lelong Numbers
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中文总结 AI 辅助
本文建立了Lelong数的精确球-固体均值公式，并据此推导出消失准则、VMO刻画及非线性容量刻画，简化了Biard-Wu全局结果证明。
中文摘要 AI 辅助
我们建立了一个精确的加性公式，该公式用多重次调和函数的球均值与固体均值之间的极限差来表达其Lelong数。基于这一恒等式，我们推导出Lelong数消失的若干等价准则，这些准则以固定尺度增量以及径向极大值、球均值、固体均值和径向正则化的渐近一致性来表述。我们还给出了零Lelong数的多重次调和函数的VMO刻画的逐点$L^1$平均振荡形式，以及Biard和Wu相应全局结果的简化证明。最后，我们建立了基于相对极值深度和深层子水平集的Bedford-Taylor容量的非线性刻画。
英文摘要
We establish an exact additive formula expressing the Lelong number of a plurisubharmonic function in terms of the limiting difference between its spherical and solid means. Building on this identity, we derive several equivalent criteria for the vanishing of the Lelong number, formulated in terms of fixed-scale increments and the asymptotic agreement of radial maxima, spherical and solid means, and radial regularizations. We also give a pointwise $L^1$ mean-oscillation formulation of the VMO characterization for plurisubharmonic functions with zero Lelong number, together with a streamlined proof of the corresponding global result of Biard and Wu. Finally, we establish a nonlinear characterization in terms of the relative extremal depth and the Bedford-Taylor capacity of deep sublevel sets.
发表机构
- University of Chinese Academy of Sciences（中国科学院大学）
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