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 …

We prove existence and regularity of metrics on a surface with boundary which maximize σ
_1 L σ 1 L where σ _1 σ 1 is the first nonzero Steklov eigenvalue and LL the boundary …

We investigate in this paper the existence of a metric which maximizes the first eigenvalue of
the Laplacian on Riemannian surfaces. We first prove that, in a given conformal class, there …

We study the existence and properties of metrics maximising the first Laplace eigenvalue
among conformal metrics of unit volume on Riemannian surfaces. We describe a general …

In this paper, we investigate critical points of the eigenvalues of the Laplace operator
considered as functionals on the space of Riemannian metrics or a conformal class of …

Given a compact surface with boundary, we introduce a family of functionals on the space of
its Riemannian metrics, defined via eigenvalues of a Steklov-type problem. We prove that …

It was proved by Montiel and Ros that for each conformal structure on a compact surface
there is at most one metric which admits a minimal immersion into some unit sphere by first …

This paper is devoted to the study of the conformal spectrum (and more precisely the first
eigenvalue) of the Laplace–Beltrami operator on a smooth connected compact Riemannian …

We prove stability estimates for the isoperimetric inequalities for the first and the second
nonzero Laplace eigenvalues on surfaces, both globally and in a fixed conformal class. We …

Maximizing the first eigenvalue on non-orientable surfaces Page 1 J. Spectr. Theory 11 (2021),
1279–1296 DOI 10.4171/JST/372 © 2021 European Mathematical Society Published by …