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 …

In this survey, we discuss some recent results on free boundary minimal surfaces in the
Euclidean unit-ball. The subject has been a very active field of research in the past few years …

In this paper we prove that any immersed stable capillary hypersurfaces in a ball in space
forms are totally umbilical. Our result also provides a proof of a conjecture proposed by …

Free boundary minimal surfaces with connected boundary and arbitrary genus Page 1 Free
boundary minimal surfaces with connected boundary and arbitrary genus Alessandro Carlotto …

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 …

In the Euclidean unit three-ball, we construct compact, embedded, two-sided free boundary
minimal surfaces with connected boundary and prescribed high genus, by a gluing …

We show that the Morse index of a properly embedded free boundary minimal hypersurface
in a strictly mean convex domain of the Euclidean space grows linearly with the dimension …

For each integer $ g\geq 1$ we use variational methods to construct in the unit $3 $-ball $ B
$ a free boundary minimal surface $\Sigma_g $ of symmetry group $\mathbb {D} _ {g+ 1} …

The topology and symmetry group of a free boundary minimal surface in the three-
dimensional Euclidean unit ball do not determine the surface uniquely. We provide pairs of …

We investigate compactness phenomena involving free boundary minimal hypersurfaces in
Riemannian manifolds of dimension less than eight. We provide natural geometric …