The anisotropic $\mathrm{\infty }$-Laplacian eigenvalue problem with Neumann boundary conditions

We analize the limit problem of the anisotropic $p$-Laplacian as $p\to \mathrm{\infty }$ with the mean of the viscosity solution. We also prove some geometric properties of eigenvalues and eigenfunctions. In particular, we show the validity of a Szeg"o-Weinberger type inequality.