2 problems

Quotient-manifold criterion. $H$ is a Banach–Lie subgroup if and only if $G/H$ carries the structure of a Banach manifold for which $q$ has a surjective differential at each point…

Let $\mathcal{F}$ be the space of initial data satisfying the prescribed boundary conditions, with $\mathcal{G}$ the space of metrics and $\mathcal{K}$ the space of momentum tensor…