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The existing proof of Wulff's theorem shows that, among all convex bodies of fixed volume, the shape given by Wulff's construction has the least surface free energy. Here it is pointed out that the restriction to convexity is unnecessary: among all bodies of fixed volume, the shape given by Wulff's construction has (uniquely) the least surface free energy. Obvious generalizations are noted.
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Johnson et al. (1965) studied this question.
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