Global Strict Monotonicity and Asymptotics of the First Steklov Eigenvalue for Regular Polygons

Zhuo Cheng, Changfeng Gui, Yeyao Hu +2

For a bounded Lipschitz planar domain $\Omega$, let ${\sigma }_1(\Omega )$ denote its first nonzero Steklov eigenvalue. Let ${\Omega }_N$ be the regular $N$-gon normalized to have perimeter $2\pi$. We prove th…