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 $m\geq 3$, and Hang-Wang and Jimenez in when $m=2$. 
D. P. Abanto, J.M. Espinar
math.AP math.DG