Abstract
In this paper we investigate Wulff shapes in $\mathbb{R}^{n+1}$ $(n\ge 0)$ from the topological viewpoint. A topological characterization of the limit of Wulff shapes and the dual Wulff shape of the given Wulff shape are provided. Moreover, we show that the given Wulff shape is never a polytope if its support function is of class $C^1$. Several characterizations of the given Wulff shape from the viewpoint of pedals are also provided. One of such characterizations may be regarded as a bridge between the mathematical aspect of crystals at equilibrium and the mathematical aspect of perspective projections.
Citation
Takashi NISHIMURA. Yu SAKEMI. "Topological aspect of Wulff shapes." J. Math. Soc. Japan 66 (1) 89 - 109, January, 2014. https://doi.org/10.2969/jmsj/06610089
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