Characterizing Stationary Logarithmic Points
AMS Southeastern Sectional Meeting, March 2013
University of Mississippi, Oxford, MS
The product of all N(N+1)/2 possible distances for a collection of N points on the circle is maximized when the points are (up to rotation) the N-th roots of unity. There is an elegant elementary proof of this fact. In higher dimensions the problem becomes much more complicated. For example, if the points are restricted to the unit sphere in 3-space, the result is known for N = 1-6, and 12. We will derive a characterization theorem for the stationary points in d-space and illustrate it with a couple of examples of optimal con gurations that are new in the literature.
Optimal configurations, logarithmic energy
Analysis | Mathematics
Peter D. Dragnev (2013).
Characterizing Stationary Logarithmic Points. Presented at AMS Southeastern Sectional Meeting, March 2013, University of Mississippi, Oxford, MS.