We investigate the Plateau and isoperimetric problems associated to Feffermans measure for strongly pseudoconvex real hypersurfaces in $mathbb C^n$ (focusing on the case $n=2$), showing in particular that the isoperimetric problem shares features of
both the euclidean isoperimetric problem and the corresponding problem in Blaschkes equiaffine geometry in which the key inequalities are reversed. The problems are invariant under constant-Jacobian biholomorphism, but we also introduce a non-trivial modified isoperimetric quantity invariant under general biholomorphism.
Building on techniques developed by Cowen and Gallardo-Guti{e}rrez, we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space $H^{2}$. We consider some specific examples, comparing our formula with several results that were previously known.
