Small eigenvalue of $\Delta$ under mean curvature flow

Question

Let $\Omega\subset R^2$ is a convex domain with smooth boundary. Evolving the $\Omega$ by evolving the $\partial \Omega$ according to $$ \partial_t X(x,t)=-H(x,t)n(x,t) $$ $n(x,t)$ is outward normal vector ,$H(x,t)$ is mean curvature, $t\ge 0$. So, I have a metabolic domain $\Omega(t)$. Then consider the small eigenvalue $$ \begin{cases} \Delta u(t) =\lambda(t) u(t) \\ u(t)|_{\partial \Omega(t)} =0 \end{cases} $$ $\Lambda(t)=\inf \lambda(t)$, then what is the sign of $\partial_t \Lambda(t)$?