Author

Jun-Cheng Wei

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Preprint Aug 2026

A positive answer to the generalized Chang-Yang conjecture on $\mathbb{S}^N$

We prove that for every integer $N\geq 3$ and $\alpha\geq \frac{1}{2}$, Beckner's inequality \[ \frac{\alpha}{2}\int_{\mathbb{S}^N}u(P_{N}u) dw+(N-1)!\int_{\mathbb{S}^N}u dw-\frac{(N-1)!}{N}\log\int_{\mathbb{S}^N}e^{Nu} dw\geq 0 \] holds for every $u\in H^{\frac{N}{2}}(\mathbb{S}^N)$ whose center of mass is at the orig...

Chang-Feng Gui, Tuo Li, Jun-Cheng Wei et al. · 0 citations

Preprint Aug 2026

Axially Symmetric Rigidity for a $Q$-Curvature-Type Equation on $ \mathbb{S}^N $

We prove that for every even integer $N\geq 4$ or $N\in\{3,5,7\}$, every axially symmetric solution to the $Q$-curvature-type problem $$ \alpha P_N u + (N-1)!(1-\frac{e^{Nu}}{\int_{\mathbb{S}^N} e^{Nu}dw})=0 \ \ \ \ \ \mbox{on} \ \mathbb{S}^N $$ is constant, provided that $ \alpha\ge\frac{1}{2}$ and $\alpha \not =1$. T...

Chang-Feng Gui, Tuo Li, Jun-Cheng Wei et al. · 0 citations