The St\"utzfunktion and the Cut Function

TL;DR

This paper explores the relationship between the Stützfunktion of convex bodies and the cut function in Minkowski space, proposing a conjectured inequality linked to cosmic censorship.

Contribution

It formalizes the connection between convex geometry and Minkowski space functions, introducing a conjecture that extends Minkowski's inequality.

Findings

Proposes a conjectured inequality for space-like two-spheres in Minkowski space.

Links the inequality to Penrose's cosmic censorship hypothesis.

Rephrases convex body theory in a formalism relating to Minkowski space functions.

Abstract

I review some standard theory of convex bodies in $\mathbb{R}^3$ and rephrase it in a formalism of Ted Newman to show the relation between the St\"utzfunktion of the former theory and the cut function introduced by Ted. This leads to a conjectured inequality for space-like two-spheres in Minkowski space that generalises Minkowski's inequality and is implied by Penrose's cosmic censorship hypothesis.