An Isodiametric Problem with Additional Constraints in Euclidean space R^3
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arXiv
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| Format: | Preprint |
| Published: |
2015
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| _version_ | 1866917817663619072 |
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| author | Yang, Yi |
| author_facet | Yang, Yi |
| contents | Let $C_θ$ be a circular cone in Euclidean space $\mathbb{R}^{3}$,which apex is the origin and apex angle of the cone is $θ\in \left(π/3, π\right)$. Let $M_θ$ be the class of compact convex domains in Euclidean space $\mathbb{R}^{3}$, which have diameter one, contains the origin and are included in $C_θ$. In this paper, we show that there is a unique compact convex domain with maximal volume and also we determine the shape of the above domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1503_03364 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | An Isodiametric Problem with Additional Constraints in Euclidean space R^3 Yang, Yi Dynamical Systems 52A40, 42A38 Let $C_θ$ be a circular cone in Euclidean space $\mathbb{R}^{3}$,which apex is the origin and apex angle of the cone is $θ\in \left(π/3, π\right)$. Let $M_θ$ be the class of compact convex domains in Euclidean space $\mathbb{R}^{3}$, which have diameter one, contains the origin and are included in $C_θ$. In this paper, we show that there is a unique compact convex domain with maximal volume and also we determine the shape of the above domain. |
| title | An Isodiametric Problem with Additional Constraints in Euclidean space R^3 |
| topic | Dynamical Systems 52A40, 42A38 |
| url | https://arxiv.org/abs/1503.03364 |