Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry
The following estimates are obtained for the diameter$D_B(I)$ and the width $\Delta_B(I)$ of isoperimetrix in Minkowski space $M^n$$$\displaystyle\frac{4v_{n-1}}{nv_n}\le \Delta_B(I)\le D_B(I)\le \displaystyle\frac{4v_{n-1}}{v_n},$$ where $v_n$ is a volume of the unit ball in $n$-dimensional Euclide...
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| Дата: | 2006 |
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| Формат: | Стаття |
| Мова: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2006
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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oai:jmag.ilt.kharkiv.ua:article-10482024-03-26T16:55:21Z Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry Diskant, V. I. isoperimetrix Minkowski geometry convex body diameter width isoperimetrix Minkowski geometry convex body diameter width The following estimates are obtained for the diameter$D_B(I)$ and the width $\Delta_B(I)$ of isoperimetrix in Minkowski space $M^n$$$\displaystyle\frac{4v_{n-1}}{nv_n}\le \Delta_B(I)\le D_B(I)\le \displaystyle\frac{4v_{n-1}}{v_n},$$ where $v_n$ is a volume of the unit ball in $n$-dimensional Euclidean space $R^n.$ The first inequality turns into equality for a bicone, the last inequality turnsinto equality for a cube.Mathematics Subject Classification 2000: 52A38, 52A40. The following estimates are obtained for the diameter$D_B(I)$ and the width $\Delta_B(I)$ of isoperimetrix in Minkowski space $M^n$$$\displaystyle\frac{4v_{n-1}}{nv_n}\le \Delta_B(I)\le D_B(I)\le \displaystyle\frac{4v_{n-1}}{v_n},$$ where $v_n$ is a volume of the unit ball in $n$-dimensional Euclidean space $R^n$ . The first inequality turns into equality for a bicone, the last inequality turnsinto equality for a cube.Mathematics Subject Classification: 52A38, 52A40. The following estimates are obtained for the diameter$D_B(I)$ and the width $\Delta_B(I)$ of isoperimetrix in Minkowski space $M^n$$$\displaystyle\frac{4v_{n-1}}{nv_n}\le \Delta_B(I)\le D_B(I)\le \displaystyle\frac{4v_{n-1}}{v_n},$$ where $v_n$ is a volume of the unit ball in $n$-dimensional Euclidean space $R^n.$ The first inequality turns into equality for a bicone, the last inequality turnsinto equality for a cube.Mathematics Subject Classification 2000: 52A38, 52A40. Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2006-12-31 Article Article application/pdf https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1048 Journal of Mathematical Physics, Analysis, Geometry; Vol. 2 No. 4 (2006); 388–395 Журнал математической физики, анализа, геометрии; Том 2 № 4 (2006); 388–395 Журнал математичної фізики, аналізу, геометрії; Том 2 № 4 (2006); 388–395 1817-5805 1812-9471 en https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1048/jm02-0388e |
| institution |
Journal of Mathematical Physics, Analysis, Geometry |
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| datestamp_date |
2024-03-26T16:55:21Z |
| collection |
OJS |
| language |
English |
| topic |
isoperimetrix Minkowski geometry convex body diameter width |
| spellingShingle |
isoperimetrix Minkowski geometry convex body diameter width Diskant, V. I. Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry |
| topic_facet |
isoperimetrix Minkowski geometry convex body diameter width isoperimetrix Minkowski geometry convex body diameter width |
| format |
Article |
| author |
Diskant, V. I. |
| author_facet |
Diskant, V. I. |
| author_sort |
Diskant, V. I. |
| title |
Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry |
| title_short |
Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry |
| title_full |
Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry |
| title_fullStr |
Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry |
| title_full_unstemmed |
Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry |
| title_sort |
estimates for diameter and width for the isoperimetrix in minkowski geometry |
| title_alt |
Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry |
| description |
The following estimates are obtained for the diameter$D_B(I)$ and the width $\Delta_B(I)$ of isoperimetrix in Minkowski space $M^n$$$\displaystyle\frac{4v_{n-1}}{nv_n}\le \Delta_B(I)\le D_B(I)\le \displaystyle\frac{4v_{n-1}}{v_n},$$ where $v_n$ is a volume of the unit ball in $n$-dimensional Euclidean space $R^n.$ The first inequality turns into equality for a bicone, the last inequality turnsinto equality for a cube.Mathematics Subject Classification 2000: 52A38, 52A40. |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України |
| publishDate |
2006 |
| url |
https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1048 |
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2025-09-26T01:40:41Z |
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2025-09-26T01:40:41Z |
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