The Characteristic Properties of the Minimal Lp-Mean Width
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...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2017/2943073 |
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| author | Tongyi Ma |
| author_facet | Tongyi Ma |
| author_sort | Tongyi Ma |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-138dcaa1bf994963aa444a5486521062 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-138dcaa1bf994963aa444a54865210622025-02-03T05:59:00ZengWileyJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/29430732943073The Characteristic Properties of the Minimal Lp-Mean WidthTongyi Ma0College of Mathematics and Statistics, Hexi University, Zhangye, Gansu 734000, ChinaGiannopoulos 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).http://dx.doi.org/10.1155/2017/2943073 |
| spellingShingle | Tongyi Ma The Characteristic Properties of the Minimal Lp-Mean Width Journal of Function Spaces |
| title | The Characteristic Properties of the Minimal Lp-Mean Width |
| title_full | The Characteristic Properties of the Minimal Lp-Mean Width |
| title_fullStr | The Characteristic Properties of the Minimal Lp-Mean Width |
| title_full_unstemmed | The Characteristic Properties of the Minimal Lp-Mean Width |
| title_short | The Characteristic Properties of the Minimal Lp-Mean Width |
| title_sort | characteristic properties of the minimal lp mean width |
| url | http://dx.doi.org/10.1155/2017/2943073 |
| work_keys_str_mv | AT tongyima thecharacteristicpropertiesoftheminimallpmeanwidth AT tongyima characteristicpropertiesoftheminimallpmeanwidth |