Electrostatic skeletons
نویسندگان
چکیده
Let u be the equilibrium potential of a compact set K in R. An electrostatic skeleton of K is a positive measure μ such that the closed support S of μ has connected complement and no interior, and the Newtonian (or logarithmic, when n = 2) potential of μ is equal to u near infinity. We prove the existence of an electrostatic skeleton for every convex polytope. Our proof raises several interesting questions on the uniqueness of a skeleton. MSC: 31A05, 31A25.
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