On Beckner's Inequality for Axially Symmetric Functions on ${\mathbb{S}}^6$

Changfeng Gui, Tuoxin Li, Juncheng Wei +1

We prove that axially symmetric solutions to the $Q$-curvature type problem $$ αP_6 u + 120(1-\frac{e^{6u}}{\int_{\mathbb{S}^6} e^{6u}})=0 \ \ \ \ \ \mbox{on} \ \mathbb{S}^6 $$ mus…