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THE GREEN–OSHER INEQUALITY IN RELATIVE GEOMETRY

Part of: General convexity

Published online by Cambridge University Press:  17 February 2016

YUNLONG YANG  and
DEYAN ZHANG
YUNLONG YANG*
Affiliation:
Department of Mathematics, Tongji University, Shanghai 200092, PR China email 88ylyang@tongji.edu.cn
DEYAN ZHANG
Affiliation:
School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, PR China email zhangdy8005@126.com
*
✉ 88ylyang@tongji.edu.cn
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Abstract

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In this paper we give a proof of the Green–Osher inequality in relative geometry using the minimal convex annulus, including the necessary and sufficient condition for the case of equality.

Keywords

Bonnesen-style inequalitiesGreen–Osher inequalitiesminimal convex annulusrelative geometrySteiner polynomials

MSC classification

Primary: 52A40: Inequalities and extremum problems
Secondary: 52A38: Length, area, volume 52A10: Convex sets in $2$ dimensions (including convex curves)

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 1 , August 2016 , pp. 155 - 164
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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