Strictly convex Wulff shapes and $C^1$ convex integrands

TL;DR

This paper establishes a precise equivalence between the strict convexity of Wulff shapes and the $C^1$ regularity of their convex integrands, with applications demonstrated.

Contribution

It proves that a Wulff shape is strictly convex if and only if its convex integrand is $C^1$, providing a new characterization and applications.

Findings

Wulff shape is strictly convex iff its integrand is $C^1$

Applications of the convex integrand regularity result

Enhanced understanding of convex shape properties

Abstract

In this paper, it is shown that a Wulff shape is strictly convex if and only if its convex integrand is of class $C^1$. Moreover, applications of this result are given.