  In this paper we prove a sharp lower bound for the first nontrivial Neumann
eigenvalue $\mu_1(\Omega)$ for the $p$-Laplace operator in a Lipschitz, bounded
domain $\Omega$ in $\R^n$. Our estimate does not require any convexity
assumption on $\Omega$ and it involves the best isoperimetric constant relative
to $\Omega$.
