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arxiv: 1309.5483 · v3 · pith:3JV2J5E6new · submitted 2013-09-21 · 🧮 math.AP

Electrostatic skeletons

Alexandre Eremenko , Erik Lundberg , Koushik Ramachandran This is my paper
classification 🧮 math.AP
keywords electrostaticpotentialskeletonwhoseclosedcompactcomplementconnected
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Let u be the equilibrium potential of a compact set K. An electrostatic skeleton of K is a positive measure whose closed support has connected complement and no interior, and whose potential is equal to u near infinity. We prove the existence of an electrostatic skeleton for any simplex.

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  1. Electrostatic skeletons and condition of strict descent

    math.CV 2026-04 unverdicted novelty 6.0

    Eremenko's conjecture is proven for convex quadrilaterals with a line of symmetry: they admit a unique electrostatic skeleton supported on a loop-free set.