We study the action of the group of contact diffeomorphisms on CR deformations of compact three dimensional CR manifolds. Using anisotropic function spaces and an anisotropic structure on the space of contact diffeomorphisms, we establish the existence of local transverse slices to the action of the contact diffeomorphism group in the neighborhood of a fixed embeddable strongly pseudoconvex CR structure.
"The Space of Cauchy-Riemann Structures on 3-D Compact Contact Manifolds." J. Differential Geom. 88 (2) 189 - 230, June 2011. https://doi.org/10.4310/jdg/1320067646