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TWO OPTIMISATION PROBLEMS FOR CONVEX BODIES

Part of: General convexity

Published online by Cambridge University Press:  05 August 2015

YUNLONG YANG  and
DEYAN ZHANG
YUNLONG YANG*
Affiliation:
Department of Mathematics, Tongji University, Shanghai 200092, PR China email [email protected]
DEYAN ZHANG
Affiliation:
Department of Mathematics, Tongji University, Shanghai 200092, PR China email [email protected]
*
✉[email protected]
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Abstract

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In this paper, we will show that the spherical symmetric slices are the convex bodies that maximise the volume, the surface area and the integral of mean curvature when the minimum width and the circumradius are prescribed and the symmetric $2$-cap-bodies are the ones which minimise the volume, the surface area and the integral of mean curvature given the diameter and the inradius.

Keywords

spherical symmetric slicesymmetric 2-cap-bodyminimum widthdiameterinradiuscircumradius

MSC classification

Primary: 52A40: Inequalities and extremum problems
Secondary: 52A15: Convex sets in $3$ dimensions (including convex surfaces)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 1 , February 2016 , pp. 137 - 145
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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