Geodesic
Smale's Conjecture on Mean Values of Polynomials and Electrostatics
Serdica Mathematical Journal, Tome 33 (2007) no. 4, pp. 399-410

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A challenging conjecture of Stephen Smale on geometry of polynomials is under discussion. We consider an interpretation which turns out to be an interesting problem on equilibrium of an electrostatic field that obeys the law of the logarithmic potential. This interplay allows us to study the quantities that appear in Smale’s conjecture for polynomials whose zeros belong to certain specific regions. A conjecture concerning the electrostatic equilibrium related to polynomials with zeros in a ring domain is formulated and discussed.
Keywords: Zeros of Polynomials, Critical Points, Smale’s Conjecture, Extremal Problem, Electrostatics 
@article{SMJ2_2007_33_4_a1,
     author = {Dimitrov, Dimitar},
     title = {Smale's {Conjecture} on {Mean} {Values} of {Polynomials} and {Electrostatics}},
     journal = {Serdica Mathematical Journal},
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     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2007_33_4_a1/}
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Dimitrov, Dimitar. Smale's Conjecture on Mean Values of Polynomials and Electrostatics. Serdica Mathematical Journal, Tome 33 (2007) no. 4, pp. 399-410. http://geodesic.mathdoc.fr/item/SMJ2_2007_33_4_a1/