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October 2015 Extremal functions for real convex bodies
Daniel M. Burns, Norman Levenberg, Sione Ma‘u
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Ark. Mat. 53(2): 203-236 (October 2015). DOI: 10.1007/s11512-014-0207-6

Abstract

We study the smoothness of the Siciak–Zaharjuta extremal function associated to a convex body in $\mathbb{R}^{2}$. We also prove a formula relating the complex equilibrium measure of a convex body in $\mathbb{R}^{n}$ (n≥2) to that of its Robin indicatrix. The main tool we use is extremal ellipses.

Funding Statement

The third author was partially supported by University of Auckland grant 3704154.

Citation

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Daniel M. Burns. Norman Levenberg. Sione Ma‘u. "Extremal functions for real convex bodies." Ark. Mat. 53 (2) 203 - 236, October 2015. https://doi.org/10.1007/s11512-014-0207-6

Information

Received: 11 December 2013; Published: October 2015
First available in Project Euclid: 30 January 2017

zbMATH: 1327.32045
MathSciNet: MR3391168
Digital Object Identifier: 10.1007/s11512-014-0207-6

Rights: 2015 © Institut Mittag-Leffler

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Vol.53 • No. 2 • October 2015
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