Compactness of isospectral conformal Finslerian metrics set on a 3-manifold

Let F be a Finslerian metric on an n-dimensional closed manifold M. In this work, we study problems about compactness of isospectral sets of conformal Finslerian metrics when n=3. More precisely, let $\widetilde{F}\in[F]$ be a Finslerian metric in the conformal class of $F$ whose scalar curvature is nonpositive constant. We show that the set of metrics in $[F]$ isospectral to $\widetilde{F}$ is compact in the $C^{\infty}$-topology.