Conformally invariant fully nonlinear elliptic equations and isolated singularities

We study properties of solutions with isolated singularities to general conformally invariant fully nonlinear elliptic equations of second order. The properties being studied include radial symmetry and monotonicity of solutions in the punctured Euclidean space and the asymptotic behavior of solutions in a punctured ball. Some results apply to more general situations including more general fully nonlinear elliptic equations of second order, and some have been used in a companion paper to establish comparison principles and Liouville type theorems for degenerate elliptic equations. (c) 2005 Elsevier Inc. All rights reserved.