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
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
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