当前位置: X-MOL 学术Constr. Approx. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Logarithmic Equilibrium on the Sphere in the Presence of Multiple Point Charges
Constructive Approximation ( IF 2.7 ) Pub Date : 2020-09-21 , DOI: 10.1007/s00365-020-09517-y
A. R. Legg , P. D. Dragnev

With the sphere $\mathbb{S}^2 \subset \mathbb{R}^3$ as a conductor holding a unit charge with logarithmic interactions, we consider the problem of determining the support of the equilibrium measure in the presence of an external field consisting of finitely many point charges on the surface of the sphere. We determine that for any such configuration, the complement of the equilibrium support is the stereographic preimage from the plane of a union of classical quadrature domains, whose orders sum to the number of point charges.

中文翻译:

多点电荷存在时球面上的对数平衡

以球体 $\mathbb{S}^2 \subset \mathbb{R}^3$ 作为持有单位电荷的导体,具有对数相互作用,我们考虑在存在外部条件时确定平衡测度的支持的问题由球体表面上的有限多个点电荷组成的场。我们确定对于任何这样的配置,平衡支持的补充是来自经典正交域联合平面的立体原像,其阶数总和为点电荷的数量。
更新日期:2020-09-21
down
wechat
bug