Sharp Finite Speed for Hyperbolic Problems Well Posed in Gevrey Classes

For linear hyperbolic operators with coefficients $a_{j,\alpha}(t,x)$ Gevrey-$s$ in $x$ and $C^k$ in $t$ with $0<k<1$ satisfying the conditions known to be sufficient to guarantee that the Cauchy problem with initial surface $\{t=0\}$ is well posed for Gevrey-$s$ data we prove two things. {\bf 1.} The domain of influence of any point $x$ on $t=0$ is contained in the union of influence curves through $x$. {\bf 2.} There is local uniqueness in the Cauchy problem for arbitrary spacelike hypersurfaces.