TWO OPTIMISATION PROBLEMS FOR CONVEX BODIES

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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Veröffentlicht in:Bulletin of the Australian Mathematical Society 2016-02, Vol.93 (1), p.137-145
Hauptverfasser: YANG, YUNLONG, ZHANG, DEYAN
Format: Artikel
Sprache:eng
Schlagworte:
Optimization
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Zusammenfassung: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