A Liouville type theorem for some conformally invariant fully nonlinear equations

Abstract

Following the approach in our earlier paper [2] and using the gradient estimates developed in [2] and [3], we give another Liouville type theorem for some conformally invariant fully nonlinear equations. Various Liouville type theorems for conformally invariant equations have been obtained by Obata, Gidas-Ni-Nirenberg, CaffarelliGidas-Spruck, Viaclovsky, Chang-Gursky-Yang, and Li-Li. For these, as well as for related works, see [2] and the references therein.For n ≥ 3, let S n×n be the set of n × n real symmetric matrices, S n×n +

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