A Problem Concerning Yamabe-Type Operators of Negative Admissible Metrics

Abstract

This paper is about a problem concerning nonlinear Yamabe-type operators of negative admissible metrics. We first give a result on ${\sigma }_k$ Yamabe problem of negative admissible metrics by virtue of the degree theory in nonlinear functional analysis and the maximum principle and then establish an existence and uniqueness theorem for the solutions to the problem.