the characteristic properties of the minimal lp-mean width
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2017
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Abstract
Giannopoulos proved that a smooth convex body K has minimal mean width position if and only if the measure hK(u)σ(du), supported on Sn-1, is isotropic. Further, Yuan and Leng extended the minimal mean width to the minimal Lp-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 Lp-mean width of convex bodies and prove the existence and uniqueness of the minimal Lp-mean width in its SL(n) images. In addition, we establish a characterization of the minimal Lp-mean width, conclude the average Mp(K) with a variation of the minimal Lp-mean width position, and give the condition for the minimum position of Mp(K).
| Reference Key |
ma2017journalthe
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| Authors | ;Tongyi Ma |
| Journal | Biosensors |
| Year | 2017 |
| DOI |
10.1155/2017/2943073
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