Activity: Talk or presentation › Talk at workshop, seminar or course › Science to science
We discuss the discrete and continuous minimal logarithmic energy problem on compact sets of revolution. We present theoretical and numerical results for finite cylinders (revolving line segments) and circular tori (revolving circles). Even these simplest cases reveal a whole host of unresolved fundamental questions about how to characterize minimal energy configurations, the asymptotics of their potential energy, their limit distribution and its support. Taking advantage of rotational symmetry, we reduce the minimum energy problem in 3-space for the singular logarithmic kernel to a plane problem for some continuous kernel. The points solving the discrete problem for the new kernel turn into the circles in the title. This is joint work with Doug Hardin and Edward B. Saff.