On the harmonic characterization of the spheres: a sharp stability inequality and some of its consequences

Giovanni Cupini, Ermanno Lanconelli

Let $D$ be a bounded open subset of ${\mathbb{R}}^n$ with $|\partial D|<\infty$ and let $x_0$ be a point of $D$. We introduce a new parameter, that we call Kuran gap of $\partial…