Author

Chang-Feng Gui

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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 Aug 2026

Optimal Rigidity Results for the $k$-Hessian Equation of Lane--Emden Type

In this paper, we establish optimal Liouville theorems and classification results for the $k$-Hessian Lane--Emden equation \[ \sigma_k(-D^2u)=u^p\quad\text{in }\R^n,\qquad -D^2u\in\overline{\Gamma_k},\qquad u\geq 0, \] where $2\leq k<\frac{n}{2}$ and $p>0$. Let $p_- = \frac{nk}{n-2k}$ and the critical Hessian--Sobo...

Wei Dai, Jingze Fu, Chang-Feng Gui et al. · 0 citations