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arXiv · 2401.03593

Simple bounds for the inradius and $\varepsilon$-inner neighbourhood of a convex body

Benedict Sewell
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Abstract

In this short note, we show that the inradius of a convex body is comparable to its volume divided by its surface area. We also give a simple formula, in terms of its volume and inradius, that is comparable to the volume of its intersection with the $\varepsilon$-neighbourhood of its boundary, and provide an application of this to self-projective attractors with convex holes.

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Benedict Sewell. 2024-01-07. Simple bounds for the inradius and $\varepsilon$-inner neighbourhood of a convex body. https://arxiv.org/abs/2401.03593

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