Asymptotics for Fully Nonlinear Equations with Isolated Singularities

We study the asymptotic behavior of solutions to subcritical ${\sigma }_k$ Yamabe equation in a punctured ball. We prove that an admissible solution to this equation with a non-removable isolated singular point is asymptotic to a radial solution. Then we are able to obtain higher order expansion of solutions using analysis of the linearized operators. These results generalize earlier pioneering work of Caffarelli, Gidas and Spruck.