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An extremal property of some capacitary measures in $ E\sb{n}$

Authors: Burgess Davis and John L. Lewis
Journal: Proc. Amer. Math. Soc. 39 (1973), 520-524
MSC: Primary 31B15
MathSciNet review: 0320347
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Abstract: The capacitary measure on an arc of the circle is known (via conformai mapping) to be that measure of a class of measures which has the largest potential at certain points of the plane. Here it is shown that the analogous result is true in $ {E_n}$.

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  • [1] L. L. Helms, Introduction to potential theory, Pure and Applied Mathematics, Vol. XXII, Wiley-Interscience A Division of John Wiley & Sons, New York-London-Sydney, 1969. MR 0261018
  • [2] J. L. Lewis, A potential theory problem in three space (to appear).
  • [3] T. J. Suffridge, A coefficient problem for a class of univalent functions, Michigan Math. J. 16 (1969), 33–42. MR 0240297

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Keywords: Capacity measure, potential
Article copyright: © Copyright 1973 American Mathematical Society

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