平面上平衡测度的矩不等式
Moment inequalities for equilibrium measures in the plane
摘要：
紧平面集的平衡测度给出了导体上电荷的稳态分布。我们表明，这种平衡测度的某些时刻，当采取的静电质心和只依赖于真正的坐标，是极值为中心的原点的间隔。这有后果的手段零的多项式，并为手段的临界点的格林函数。我们还研究了矩取决于质心的距离，如静电惯性矩。
英文摘要：
The equilibrium measure of a compact plane set gives the steady state distribution of charges on the conductor. We show that certain moments of this equilibrium measure, when taken about the electrostatic centroid and depending only on the real coordinate, are extremal for an interval centered at the origin. This has consequences for means of zeros of polynomials, and for means of critical points of Green's functions. We also study moments depending on the distance from the centroid, such as the electrostatic moment of inertia.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
