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

Full-text: Open access

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.

Note

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

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485802714

Digital Object Identifier
doi:10.1007/s11512-014-0207-6

Mathematical Reviews number (MathSciNet)
MR3391168

Zentralblatt MATH identifier
1327.32045

Rights
2015 © Institut Mittag-Leffler

Citation

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. https://projecteuclid.org/euclid.afm/1485802714


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