A spherical flatness index and a stability inequality for harmonic pseudospheres

Andrea Buffoni, Giovanni Cupini, Ermanno Lanconelli

We introduce a new flatness index for the boundary of an open subset $\hat{I}\text{c◯}$ of ${\mathbb{R}}^n$, $n\ge 2$. This index provides a necessary condition for $\partial \hat{I}\text{c◯}$ to be a harmonic p…