Q-curvature flow with indefinite nonlinearity

Abstract

Abstract. In this note, we study Q-curvature flow on S 4 with indefinite nonlinearity. Our result is that the prescribed Q-curvature problem on S 4 has a solution provided the prescribed Q-curvature f has its positive part, which possesses non-degenerate critical points such that ∆ S 4 f = 0 at the saddle points and an extra condition such as a nontrivial degree counting condition.

Prescribing <inline-formula><tex-math id="M1">\begin{document}$ Q $\end{document}</tex-math></inline-formula>-curvature on <inline-formula><tex-math id="M2">\begin{document}$ S^n $\end{document}</tex-math></inline-formula> in the presence of symmetry

“…where α is chosen such that the volume is preserved along the flow. See [3,12,20,22,23,26,27] for results related to the Q-curvature flow.…”