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This is equivalent to the following result: If all critical points of a rational function lie on a circle in the Riemann sphere (for example, on the real line), then the function maps this circle into ...
Tsai-Han Kiang, On the Existence of Critical Points of Green's Functions for Three-Dimensional Regions, American Journal of Mathematics, Vol. 54, No. 4 (Oct., 1932), pp. 657-666 ...
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