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
MathSciNet review:
3665051
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Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
232641
Email:
nishimura-takashi-yx@ynu.jp
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
