Self-dual Wulff shapes and spherical convex bodies of constant width ${\pi}/{2}$

TL;DR

This paper establishes a precise equivalence between self-dual Wulff shapes and spherical convex bodies of constant width π/2, linking geometric duality with constant width properties.

Contribution

It proves that a Wulff shape is self-dual if and only if its associated spherical convex body has constant width π/2, providing a new characterization of self-duality.

Findings

Self-dual Wulff shapes correspond to spherical convex bodies of constant width π/2.

The paper provides a geometric criterion for self-duality in terms of spherical convex bodies.

This characterization bridges Wulff shape duality with spherical convex geometry.

Abstract

For any Wulff shape, its dual Wulff shape is naturally defined. A self-dual Wulff shape is a Wulff shape equaling its dual Wulff shape exactly. In this paper, it is shown that a Wulff shape is self-dual if and only if the spherical convex body induced by it is of constant width ${\pi}/{2}$.