The monotonicity of the Cheeger constant for parallel bodies

Ilias Ftouhi

We prove that for every planar convex set $\Omega$, the function $t\in (-r(\Omega ),+\infty )⟼\sqrt{|{\Omega }_t|}h({\Omega }_t)$ is monotonically decreasing, where $r$, $|\cdot |$ and $h$ stand for…