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

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 $\epsilon$-neighbourhood of its boundary, and provide an application of this to self-projective attractors with convex holes.

8 pages; 3 figures