Pingxin Gu

Isodiametric-type upper bounds for Steklov eigenvalues

Let $n\geq 2$. We establish isodiametric-type upper bounds for Steklov eigenvalues of bounded Lipschitz domains $\Omega$ in Euclidean space $\mathbb{R}^n$ and hyperbolic space $\mathbb{H}^n$. In Euclidean space, we prove \[ D(\Omega)\sigma_k(\Omega)\leq C(n)k, \] with optimal dependence on $k$. For domains in either $\...