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arXiv · 1503.03364

An Isodiametric Problem with Additional Constraints in Euclidean space R^3

Yi Yang
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Abstract

Let $C_{\theta}$ be a circular cone in Euclidean space $\mathbb{R}^{3}$,which apex is the origin and apex angle of the cone is $\theta\in \left(\pi/3, \pi\right)$. Let $M_\theta$ be the class of compact convex domains in Euclidean space $\mathbb{R}^{3}$, which have diameter one, contains the origin and are included in $C_{\theta}$. 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.

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Yi Yang. 2015-03-11. An Isodiametric Problem with Additional Constraints in Euclidean space R^3. https://arxiv.org/abs/1503.03364

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