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Extremal functions for real convex bodies

Daniel M. Burns Department of Mathematics, University of Michigan Norman Levenberg Department of Mathematics, Indiana University Sione Ma‘u Department of Mathematics, University of Auckland

Convex and Discrete Geometry mathscidoc:1701.40001

Arkiv for Matematik, 53, (2), 203-236, 2013.12
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.
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@inproceedings{daniel2013extremal,
  title={Extremal functions for real convex bodies},
  author={Daniel M. Burns, Norman Levenberg, and Sione Ma‘u},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203640388500082},
  booktitle={Arkiv for Matematik},
  volume={53},
  number={2},
  pages={203-236},
  year={2013},
}
Daniel M. Burns, Norman Levenberg, and Sione Ma‘u. Extremal functions for real convex bodies. 2013. Vol. 53. In Arkiv for Matematik. pp.203-236. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203640388500082.
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