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


Authors: Huhe Han and Takashi Nishimura
Journal: Proc. Amer. Math. Soc. 145 (2017), 3997-4008
MSC (2010): Primary 52A20, 52A55, 82D25
DOI: https://doi.org/10.1090/proc/13510
Published electronically: April 7, 2017
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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.


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Additional Information

Huhe Han
Affiliation: Graduate School of Environment and Information Sciences,Yokohama National University, Yokohama 240-8501, Japan
Email: han-huhe-bx@ynu.jp

Takashi Nishimura
Affiliation: Research Institute of Environment and Information Sciences, Yokohama National University, Yokohama 240-8501, Japan
Email: nishimura-takashi-yx@ynu.jp

DOI: https://doi.org/10.1090/proc/13510
Keywords: Wulff shape, convex integrand, convex body, dual Wulff shape, spherical Wulff shape, spherical convex body, spherical dual Wulff shape.
Received by editor(s): January 24, 2016
Received by editor(s) in revised form: September 22, 2016, and September 26, 2016
Published electronically: April 7, 2017
Communicated by: Ken Ono
Article copyright: © Copyright 2017 American Mathematical Society

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