Non-preservation of $\alpha$-concavity for the porous medium equation in higher dimensions

In this short note, we prove that [Formula: see text]-concavity of the pressure is not preserved for the porous medium equation in dimensions [Formula: see text] and higher for any [Formula: see text]. Together with the result of Chau-Weinkove for [Formula: see text], this fully resolves an open problem posed by Vásquez on whether pressure concavity is preserved in general for the porous medium equation.