Arkiv för Matematik

  • Ark. Mat.
  • Volume 53, Number 2 (2015), 203-236.

Extremal functions for real convex bodies

Daniel M. Burns, Norman Levenberg, and Sione Ma‘u

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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.


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

Article information

Ark. Mat., Volume 53, Number 2 (2015), 203-236.

Received: 11 December 2013
First available in Project Euclid: 30 January 2017

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2015 © Institut Mittag-Leffler


Burns, Daniel M.; Levenberg, Norman; Ma‘u, Sione. Extremal functions for real convex bodies. Ark. Mat. 53 (2015), no. 2, 203--236. doi:10.1007/s11512-014-0207-6.

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