TWO OPTIMISATION PROBLEMS FOR CONVEX BODIES

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...

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Bibliographic Details
Published inBulletin of the Australian Mathematical Society Vol. 93; no. 1; pp. 137 - 145
Main Authors YANG, YUNLONG, ZHANG, DEYAN
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.02.2016
Subjects
Optimization
secondary 52A15
inradius
diameter
primary 52A40
symmetric 2-cap-body
spherical symmetric slice
circumradius
minimum width
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Summary: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.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972715000799