Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 397-401

ELECTROSTATIC SKELETONS

Erik Lundberg and Koushik Ramachandran

Florida Atlantic University, Department of Mathematical Sciences
Boca Raton, FL 33431, U.S.A.; elundber 'at' fau.edu

Indian Statistical Institute, Theoretical Statistics and Mathematics Unit
Bangalore 560 059, India; kram_vs 'at' isibang.ac.in

Abstract. Let P be the equilibrium potential of a compact set K in Rⁿ. An electrostatic skeleton of K is a positive measure μ such that the closed support S of μ has connected complement and empty interior, and the Newtonian (or logarithmic, when n = 2) potential of μ is equal to P near infinity. We prove the existence and uniqueness of an electrostatic skeleton for any simplex.

2010 Mathematics Subject Classification: Primary 31A12, 31A25.

Key words: Potential, equilibrium, subharmonic function, inverse problem, analytic continuation.

Reference to this article: E. Lundberg and K. Ramachandran: Electrostatic skeletons. Ann. Acad. Sci. Fenn. Math. 40 (2015), 397-401.

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doi:10.5186/aasfm.2015.4020