Maximum and minimum of support functions

For given continuous functions $γ_{{}_{i}}: S^{n}\to \mathbb{R}_{+}$ (where $i=1, 2$), the functions $γ_{{}_{max}}$ and $γ_{{}_{min}}$ can be defined as natural way. In this paper, we show that the Wulff shape associated to $γ_{{}_{max}}$ is the convex hull of the union of Wulff shapes associated to $γ_{{}_1}$ and $γ_{{}_2}$ , if $γ_{{}_1}$ and $γ_{{}_2}$ are convex integrands. And, the Wulff shape associated to $γ_{{}_{min}}$ is the intersection of Wulff shapes associated to $γ_{{}_1}$ and $γ_{{}_2}$. Moreover, relationships between their dual Wulff shapes are given.

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