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 …

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 …

Using methods in the spirit of deterministic homogenisation theory we obtain convergence of
the Steklov eigenvalues of a sequence of domains in a Riemannian manifold to weighted …

It was conjectured by Escobar (J Funct Anal 165: 101–116, 1999) that for an n-dimensional
(n≥ 3) smooth compact Riemannian manifold with boundary, which has nonnegative Ricci …

We consider the magnetic Steklov eigenvalue problem on compact Riemannian manifolds
with boundary for generic magnetic potentials and establish various results concerning the …

In this paper we obtain several results concerning the optimization of higher Steklov
eigenvalues both in two and higher dimensional cases. We first show that the normalized …

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 …

Sharp Steklov Upper Bound for Submanifolds of Revolution | The Journal of Geometric
Analysis Skip to main content Springer Nature Link Account Menu Find a journal Publish …

Abstract Let M n=[0, R]× S n-1 be an n-dimensional (n≥ 2) smooth Riemannian manifold
equipped with the warped product metric g= dr 2+ h 2 (r) g S n-1 and diffeomorphic to a …

We consider the Steklov eigenvalue problem on a compact pinched negatively curved
manifold of dimension at least three with totally geodesic boundaries. We obtain a geometric …