# Constant diameter and constant width of spherical convex bodies

## TL;DR

This paper proves that spherical convex bodies with constant diameter also have constant width, establishing an equivalence for 0<τ<π, and explores applications to Wulff shapes.

## Contribution

It demonstrates the equivalence between constant diameter and constant width in spherical convex bodies, extending understanding in spherical convex geometry.

## Key findings

- Constant diameter implies constant width in spherical convex bodies.
- The equivalence holds for 0<τ<π.
- Applications to Wulff shapes are provided.

## Abstract

In this paper we show that a spherical convex body $C$ is of constant diameter $\tau$ if and only if $C$ is of constant width $\tau$, for $0<\tau<\pi$. Moreover, some applications to Wulff shapes are given.