Singularity and decay estimates for the conformal k-hessian equation via Liouville-type theorems

Abstract

We study some connections between Liouville type theorems and local properties of nonnegative solutions to conformal k-hessian equations by making use of an elementary lemma for all positive functions in Li and Zhang (J. Anal. Math. 90 (2003), 27-87) and related Liouville type theorems in Li and Li (Acta. Math. 195 (2005), 117-154). Mathematics Subject Classification (2000). Primary 36J60, Secondary 35B65.