Let $\Omega$ be a bounded, convex open subset of $\mathbb{R}^n$. Let $p>1$ and let $F:\mathbb{R}^n\rightarrow[0,+\infty)$ be a Finsler norm. In this paper we study a particular anisotropic and scale invariant functional in the form: $$\mathcal{F}(\Omega)=\dfrac{\displaystyle\int_{\partial \Omega} [F^o(x) ]^p\;F(\nu_{\partial\Omega}(x))\;d\mathcal{H}^{n-1}(x) }{P_F(\Omega)V(\Omega)^{\frac{p}{n}}};$$ we call anisotropic $p-$momentum the quantity $M_{F}(\Omega):=\int_{\partial \Omega} [F^o(x) ]^p\;F(\nu_{\partial\Omega}(x))\;d\mathcal{H}^{n-1}(x) ,$ where $F^o$ is the polar function of $F$ and $\nu_{\partial \Omega}$ is the outward unit normal to $\partial\Omega$. By $V(\Omega)$ and $P_F(\Omega)$ we denote respectively the volume of $\Omega$ and its anisotropic perimeter, i.e. $ P_F(\Omega)=\int_{\partial \Omega}F(\nu_{\partial\Omega}(x))\;d\mathcal{H}^{n-1}(x).$ We show that the Wulff shape, associated with the Finsler norm $F$ considered and centered at the origin, is the unique mini 查看全文>>