Journal of the Mathematical Society of Japan

Self-dual Wulff shapes and spherical convex bodies of constant width ${\pi}/{2}$

Huhe HAN and Takashi NISHIMURA

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For any Wulff shape, its dual Wulff shape is naturally defined. A self-dual Wulff shape is a Wulff shape equaling its dual Wulff shape exactly. In this paper, it is shown that a Wulff shape is self-dual if and only if the spherical convex body induced by it is of constant width ${\pi}/{2}$.

Article information

J. Math. Soc. Japan, Volume 69, Number 4 (2017), 1475-1484.

First available in Project Euclid: 25 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 52A55: Spherical and hyperbolic convexity

Wulff shape dual Wulff shape self-dual Wulff shape spherical convex body width constant width Lune thickness diameter spherical polar set


HAN, Huhe; NISHIMURA, Takashi. Self-dual Wulff shapes and spherical convex bodies of constant width ${\pi}/{2}$. J. Math. Soc. Japan 69 (2017), no. 4, 1475--1484. doi:10.2969/jmsj/06941475.

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