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$(M,F:=\\sqrt{g}+\\beta)$, where $g$ is a Riemannian metric on $M$ and $\\beta$ an appropriate $1$-form on $M$, it is shown that the first eigenvalue $\\lambda_{1,p}(M,F)$ of the Finslerian $p$-Laplacian defined by the Finsler metric $F$ is controled by the first eigenvalue $\\lambda_{1,p}(M,g)$ of the Riemannian $p$-Laplacian 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