论文标题
在球体上的对称位置电荷的矢量平衡问题
A vector equilibrium problem for symmetrically located point charges on a sphere
论文作者
论文摘要
我们研究了在北极周围对称的R+1相等点电荷产生的外部场上，在二维球上的平衡度量。平衡度量的支持称为液滴。液滴具有一个母体，我们通过矢量平衡问题（VEP）来表征复杂平面中的R度量。 该模型经历了两个转变，这些转变反映在VEP最小化器的第一个组件的支持中，即支持可以是包含0的有限间隔，两个间隔的结合或全半路。两个间隔情况对应于具有两个不相交成分的液滴，并通过一个riemann属表面进行分析。
We study the equilibrium measure on the two dimensional sphere in the presence of an external field generated by r+1 equal point charges that are symmetrically located around the north pole. The support of the equilibrium measure is known as the droplet. The droplet has a motherbody which we characterize by means of a vector equilibrium problem (VEP) for r measures in the complex plane. The model undergoes two transitions which is reflected in the support of the first component of the minimizer of the VEP, namely the support can be a finite interval containing 0, the union of two intervals, or the full half-line. The two interval case corresponds to a droplet with two disjoint components, and it is analyzed by means of a genus one Riemann surface.
