Extremal properties of Green functions and A. Weitsman’s conjecture
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- by Alexander Fryntov PDF
- Trans. Amer. Math. Soc. 345 (1994), 511-525 Request permission
Abstract:
A new version of the symmetrization theorem is proved. Using a modification of the $\ast$-function of Baernstein we construct an operator which maps a family of $\delta$-subharmonic functions defined on an annulus into a family of subharmonic functions on an annular sector. Applying this operator to the Green function of special domains we prove A. Weitsman’s conjecture linked with exact estimates of the Green functions of these domains.References
- Albert Baernstein II, Integral means, univalent functions and circular symmetrization, Acta Math. 133 (1974), 139–169. MR 417406, DOI 10.1007/BF02392144
- Albert Baernstein II, An extremal problem for certain subharmonic functions in the plane, Rev. Mat. Iberoamericana 4 (1988), no. 2, 199–218. MR 1028739, DOI 10.4171/RMI/71
- A. E. Fryntov, An extremal problem of potential theory, Dokl. Akad. Nauk SSSR 300 (1988), no. 4, 819–820 (Russian); English transl., Soviet Math. Dokl. 37 (1988), no. 3, 754–755. MR 950785 W. K. Hayman and P. B. Kennedy, Subharmonic functions, Academic Press, San Diego, 1976. A. Weitsman, Some remarks on the spread of a Nevanlinna deficiency, Mittag-Leffler Technical report No. 7, 1977.
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 345 (1994), 511-525
- MSC: Primary 31A05
- DOI: https://doi.org/10.1090/S0002-9947-1994-1181183-7
- MathSciNet review: 1181183