3 papers
math.AP2026
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 .…
math.AP2025
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…
math.AP2025
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…