Escobar's Type Theorems for elliptic fully nonlinear degenerate equations

In this paper we prove non-existence and classification results for elliptic fully nonlinear elliptic degenerate conformal equations on certain subdomains of the sphere with prescribed constant mean curvature along its boundary. We also consider non-degenerate equations. Such subdomains are the hemisphere (or a geodesic ball in ${\mathbb{S}}^m$), punctured balls and annular domains. Our results extend those of Escobar in when $m\ge 3$, and Hang-Wang and Jimenez in when $m=2$.