Extremal problems related to Gauss-John position

Li, Ai Jun; Leng, Gang Song

doi:10.1007/s10114-012-9735-9

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“…Li and Leng [14] showed that let L be a given convex body in n  and K be a convex body such that o K L ∈ ⊆ . If K is in extremal position of (1.2), then…”

Section: Introductionmentioning

confidence: 99%

Extremal Problems Related to Dual Gauss-John Position

Zhangye¹

2018

JAMP

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In this paper, the extremal problem, min{ () : , GL()} p l K o K L n φ φ φ ∈ ⊆ ∈  , of two convex bodies K and L in n  is considered. For K to be in extremal position in terms of a decomposition of the identity, give necessary conditions together with the optimization theorem of John. Besides, we also consider the weaker optimization problem: 1 2 give the geometric distance between the unit ball 2 n B and a centrally symmetric convex body K.

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“…Li and Leng [14] showed that let L be a given convex body in n  and K be a convex body such that o K L ∈ ⊆ . If K is in extremal position of (1.2), then…”

Section: Introductionmentioning

confidence: 99%

Extremal Problems Related to Dual Gauss-John Position

Zhangye¹

2018

JAMP

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The Characteristic Properties of the Minimal Lp-Mean Width

2017

Journal of Function Spaces

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Giannopoulos proved that a smooth convex body has minimal mean width position if and only if the measure ℎ ( ) (d ), supported on −1 , is isotropic. Further, Yuan and Leng extended the minimal mean width to the minimal -mean width and characterized the minimal position of convex bodies in terms of isotropicity of a suitable measure. In this paper, we study the minimal -mean width of convex bodies and prove the existence and uniqueness of the minimal -mean width in its SL( ) images. In addition, we establish a characterization of the minimal -mean width, conclude the average ( ) with a variation of the minimal -mean width position, and give the condition for the minimum position of ( ).

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Extremal problems related to Gauss-John position

Cited by 2 publications

References 9 publications

Extremal Problems Related to Dual Gauss-John Position

Extremal Problems Related to Dual Gauss-John Position

The Characteristic Properties of the Minimal Lp-Mean Width

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