Application of spherical convex bodies to Wulff shape

TL;DR

This paper explores geometric properties of convex bodies on spheres and applies these findings to identify self-dual Wulff shapes in Euclidean space, advancing understanding in convex and surface shape analysis.

Contribution

It introduces new relationships between diameter, width, and thickness of convex bodies on spheres and applies them to characterize self-dual Wulff shapes.

Findings

Established relationships between geometric measures on spherical convex bodies.

Provided criteria for recognizing self-dual Wulff shapes.

Enhanced methods for analyzing convex shapes in Euclidean space.

Abstract

We present some relationships between the diameter, width and thickness of a reduced convex body on the $d$-dimensional sphere. We apply the obtained properties to recognize if a Wulff shape in the Euclidean $d$-space is self-dual.