Minimum Energy Problem on the Hypersphere

作者：Bilogliadov Mykhailo^*

来源：Potential Analysis, 2018, 48(1): 49-84.

DOI：10.1007/s11118-017-9626-x

• Minimum energy problem
• Newtonian potential
• Weighted energy
• Equilibrium measure
• Extremal measure

We consider the minimum energy problem on the unit sphere in the Euclidean space , d = 3, in the presence of an external field Q, where the charges are assumed to interact according to Newtonian potential 1/r (d-2), with r denoting the Euclidean distance. We solve the problem by finding the support of the extremal measure, and obtaining an explicit expression for the density of the extremal measure. We then apply our results to an external field generated by a point charge of positive magnitude, placed at the North Pole of the sphere, and to a quadratic external field.

• 出版日期2018-1