2 problems

Let $\Sigma$ be a smooth surface with smooth boundary, endowed with a Riemannian metric. Let $\varkappa$ denote the boundary operator and $D_\Sigma$ the Dirichlet-to-Neumann operat…

Let $\Sigma$ be a surface with disconnected boundary $\partial\Sigma$, and let $g$ be a maximizer of the normalized first Steklov eigenvalue $\bar{\sigma}_1(\Sigma,\cdot)$. Define…