Related papers: Bifurcating nodoids

We are concerned with hypersurfaces of $\mathbb{R}^N$ with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter under a volume constraint. Our results are twofold.…

We show that some pieces of cylinders bounded by two parallel straight-lines bifurcate in a family of periodic non-rotational surfaces with constant mean curvature and with the same boundary conditions. These cylinders are initial…

We consider constant mean curvature surfaces (invariant by a continuous group of isometries) lying at bounded distance from a horizontal geodesic on any homogeneous $3$-manifold $\mathbb{E}(\kappa,\tau)$ with isometry group of dimension…

We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form $H(X)=1+{A}{|X|^{-\gamma}}$ for $|X|$ large, when $A<0$ and…

It is known that for any non-zero $M in (-1/4,infty)$, if we roll the conic {(x,y): 4 x^2-y^2/M}=1} on a line in a plane, and then we rotate about this line the trace of a focus, then we obtain a surface of revolution D(M) with mean…

Let S be a compact connected surface and let f be an element of the group Homeo\_0(S) of homeomorphisms of S isotopic to the identity. Denote by \tilde{f} a lift of f to the universal cover of S. Fix a fundamental domain D of this universal…

We introduce a class of complex surface singularities - the blow-$ADE$ singularities - which are likely to be stable with respect to $\mu^*$-constant deformations. We prove such a stability property in several special cases. Here, we…

We classify constant mean curvature surfaces invariant by a 1-parameter group of isometries in the Berger spheres and in the special linear group Sl(2, R). In particular, all constant mean curvature spheres in those spaces are described…

We derive parametrizations of the Delaunay constant mean curvature surfaces of revolution that follow directly from parametrizations of the conics that generate these surfaces via the corresponding roulette. This uniform treatment exploits…

We consider stable minimal surfaces of genus 1 in Euclidean space and in Riemannian manifolds. Under the condition of covering stability (all finite covers are stable) we show that a genus 1 finite total curvature minimal surface in…

Motivated by the large ammount of results obtained for minimal and positive constant mean curvature surfaces in several ambient spaces, the aim of this paper is to obtain half-space theorems for properly immersed surfaces in $\mathbb{R}^3$…

We obtain compact orientable embedded surfaces with constant mean curvature $0<H<\frac{1}{2}$ and arbitrary genus in $\mathbb{S}^2\times\mathbb{R}$. These surfaces have dihedral symmetry and desingularize a pair of spheres with mean…

We consider constant mean curvature surfaces of finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were constructed and completely classified by the authors in…

Four constructions of constant mean curvature (CMC) hypersurfaces in the (n+1)-sphere are given, which should be considered analogues of `classical' constructions that are possible for CMC hypersurfaces in Euclidean space. First,…

The collection of all non-degenerate, continuous, two-piece, piecewise-linear maps on $\mathbb{R}^2$ can be reduced to a four-parameter family known as the two-dimensional border-collision normal form. We prove that throughout an open…

We study the topology of analytic families of $n$-dimensional complex hypersurfaces having an isolated singularity at the origin. We prove that such a family is $\mu$-constant if and only if it admits an uniform Milnor radius, which happens…

Let $\mathcal X\to\mathbb D$ be a flat family of projective complex 3-folds over a disc $\mathbb D$ with smooth total space $\mathcal X$ and smooth general fibre $\mathcal X_t,$ and whose special fiber $\mathcal X_0$ has double normal…

We construct a one-parameter family of properly embedded minimal annuli in the Heisenberg group Nil_3 endowed with a left-invariant Riemannian metric. These annuli are not rotationally invariant. This family gives a vertical half-space…

We announce the classification of complete, almost embedded surfaces of constant mean curvature, with three ends and genus zero: they are classified by triples of points on the sphere whose distances are the asymptotic necksizes of the…

In this paper we shall establish that properly embedded constant mean curvature one surfaces in H^3 of finite topology are of finite total curvature and each end is regular. In particular, this implies the horosphere is the only simply…