Author

Ye-Yao Hu

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Preprint Sep 2026

The P\'olya--Szeg\H{o} conjecture for convex polygons with many sides

For every sufficiently large N, we prove that the regular N-gon uniquely minimizes the first Dirichlet eigenvalue among convex polygons of prescribed area with at most N sides, up to rigid motions. Quantitative Faber--Krahn stability localizes minimizers near the disk but leaves their discrete geometry undetermined. We...

Zhuo Cheng, Chang-Feng Gui, Ye-Yao Hu et al. · 0 citations

Preprint Oct 2026

Rigidity of a $Q$-curvature-type problem on $\mathbb{S}^N$ in every dimension $N\geq3$

We prove that for every $N\geq 3$, every solution to the $Q$-curvature-type problem $$ \alpha P_N u + (N-1)!\left(1-\frac{e^{Nu}}{\int_{\mathbb{S}^N} e^{Nu}dw}\right)=0 \ \ \ \ \ \mbox{on} \ \mathbb{S}^N $$ is constant, provided that $ \alpha\ge\frac{1}{2}$ and $\alpha \not =1$. The proof consists of a spectral gap est...

Chang-Feng Gui, Ye-Yao Hu, Tuo Li et al. · 0 citations