Extremal functions for real convex bodies: simplices, strips, and ellipses

TL;DR

This paper introduces a method to compute extremal functions for real convex bodies like simplices, strips, and ellipses, providing new insights into their geometric and analytic properties.

Contribution

It offers an explicit computational approach for extremal functions of convex polytopes and proves the existence of extremal ellipses for these bodies.

Findings

Explicit method for extremal function computation

New proof of extremal ellipses existence

Enhanced understanding of convex body extremal functions

Abstract

We present an explicit method to compute the (Siciak-Zaharjuta) extremal function of a real convex polytope in terms of supporting simplices and strips. We use this to give a new proof of the existence of extremal ellipses associated to the extremal function of a real convex body.