6 papers
A quantitative Robin Pólya--Szegő theorem for tangential polygons
Changfeng Gui, Yeyao Hu, Qinfeng Li +1
We extend the quantitative Dirichlet theorem of Gui, Hu, and Li \cite{GuiHuLi2026} to Robin torsional rigidity. For every fixed , we prove that the regular -gon uniquely ma…
Serrin's Problem under Dirichlet Perturbations: Geometric Compactness and Sharp Planar Stability
Qinfeng Li, Weihong Xie, Hang Yang
In earlier work [21], we posed a stability question for Serrin's overdetermined problem under Dirichlet perturbations and proved that the answer is negative in dimensions .…
Flow approach on Riesz type nonlocal energies
Jiaxin He, Qinfeng Li, Juncheng Wei +1
Via continuous deformations based on natural flow evolutions, we prove several novel monotonicity results for Riesz-type nonlocal energies on triangles and quadrilaterals. Some of…
A flow approach to the monotonicity of shape functionals
Yong Huang, Qinfeng Li, Shuangquan Xie +1
We develop a geometric flow framework to investigate two classical shape functionals: the torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. First, by construc…
On the location of the maximal gradient of the torsion function over some non-symmetric planar domains
Qinfeng Li, Shuangquan Xie, Hang Yang +1
We investigate the location of the maximal gradient of the torsion function on certain non-symmetric planar domains. First, by establishing uniform estimates for convex narrow doma…
Torsion energy with boundary mean zero condition
Qinfeng Li, Weihong Xie, Hang Yang
Motivated by establishing Neumann Talenti type comparison results, we concern the minimization of the following shape functional under volume constraint: \begin{align*} T(Ω):=\inf\…