The Steklov eigenvalue problem, first introduced over 125 years ago, has seen a surge of
interest in the past few decades. This article is a tour of some of the recent developments …

The Steklov problem is an eigenvalue problem with the spectral parameter in the boundary
conditions, which has various applications. Its spectrum coincides with that of the Dirichlet-to …

How close is the Dirichlet-to-Neumann (DtN) map to the square root of the corresponding
boundary Laplacian? This question has been actively investigated in recent years …

We obtain upper and lower bounds for Steklov eigenvalues of submanifolds with prescribed
boundary in Euclidean space. A very general upper bound is proved, which depends only …

This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing
mathematics of symmetry. Instead of breaking up patterns into blocks—a sort of potato …

The validity of Weyl's law for the Steklov problem on domains with Lipschitz boundary is a
well-known open question in spectral geometry. We answer this question in two dimensions …

Given two compact Riemannian manifolds M 1 and M 2 such that their respective
boundaries Σ 1 and Σ 2 admit neighbourhoods Ω 1 and Ω 2 which are isometric, we prove …

Let $(M, g) $ be a compact Riemannian manifold with boundary. Let $ b> 0$ be the number
of connected components of its boundary. For manifolds of dimension $\geq 3$, we prove …

Let $(\Omega, g) $ be a real analytic Riemannian manifold with real analytic boundary
$\partial\Omega $. Let $\psi_ {\lambda} $ be an eigenfunction of the Dirichlet-to-Neumann …

Consider a compact Riemannian manifold with boundary. In this short note we prove that
under certain positive curvature assumptions on the manifold and its boundary the Steklov …