Uniqueness theorems for fully nonlinear conformal equations on subdomains of the sphere

Abstract In this paper we prove classification results to elliptic fully nonlinear conformal equations in certain subdomains of the sphere with prescribed constant mean curvature on its boundary. Such subdomains are the hemisphere (or a geodesic ball in S n ) of dimension n ≥ 2 with prescribed constant mean curvature on its boundary, and annular domains with minimal boundary. Our results extend previous ones concerning more general curvature functions on the eigenvalues of the Schouten tensor than scalar curvature.