Author

Qin-Feng Li

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Preprint Oct 2026

A quantitative Robin P\'olya--Szeg\H{o} theorem for tangential polygons

We extend the quantitative Dirichlet theorem of Gui, Hu, and Li \cite{GuiHuLi2026} to Robin torsional rigidity. For every fixed $\beta>0$, we prove that the regular $N$-gon uniquely maximizes Robin torsional rigidity among tangential $N$-gons of prescribed area. Our explicit perimeter deficit bound contains the Dirichl...

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

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