Related papers: Area-stationary surfaces inside the sub-Riemannian…

We explore various notions of stability for surfaces embedded and immersed in spacetimes and initial data sets. The interest in such surfaces lies in their potential to go beyond the variational techniques which often underlie the study of…

We obtain a classification result for rotational surfaces in the Heisenberg space and the universal cover of the special linear group, whose mean curvature is given as a prescribed $C^1$ function depending on their angle function. We show…

We classify complete orientable hypersurfaces of constant isotropic curvature in space forms. We show that such a hypersurface has constant mean curvature only if it is an isoparametric hypersurface, and that it is minimal if and only if it…

We study surfaces in TN that are area-stationary with respect to a neutral Kaehler metric constructed on TN from a riemannian metric g on N. We show that holomorphic curves in TN are area-stationary, while lagrangian surfaces that are…

The first author studied spacelike constant mean curvature one (CMC-1) surfaces in de Sitter 3-space when the surfaces have no singularities except within some compact subset and are of finite total curvature on the complement of this…

Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the…

We start the investigation of immersions $\Psi$ of a simply connected domain $D$ into three dimensional Euclidean space $R^3$, which have constant mean curvature (CMC-immersions), and allow for a group of automorphisms of $D$ which leave…

For spacelike stationary (i.e. zero mean curvature) surfaces in 4-dimensional Lorentz space one can naturally introduce two Gauss maps and Weierstrass representation. In this paper we investigate their global geometry systematically. The…

We prove that finite area isolated singularities of surfaces with constant positive curvature in R^3 are removable singularities, branch points or immersed conical singularities. We describe the space of immersed conical singularities of…

We define discrete constant mean curvature (cmc) surfaces in the three-dimensional Euclidean and Lorentz spaces in terms of sphere packings with orthogonally intersecting circles. These discrete cmc surfaces can be constructed from…

Consider a sequence of closed, orientable surfaces of fixed genus $g$ in a Riemannian manifold $M$ with uniform upper bounds on mean curvature and area. We show that on passing to a subsequence and choosing appropriate parametrisations, the…

We describe the curves of constant (geodesic) curvature and torsion in the three-dimensional round sphere. These curves are the trajectory of a point whose motion is the superposition of two circular motions in orthogonal planes. The global…

It is still an open question whether a compact embedded hypersurface in the Euclidean space R^{n+1} with constant mean curvature and spherical boundary is necessarily a hyperplanar ball or a spherical cap, even in the simplest case of…

In this paper we study several aspects of the geometry of conformally stationary Lorentz manifolds, and particularly of GRW spaces, due to the presence of a closed conformal vector field. More precisely, we begin by extending to these…

We study the classification of immersed constant mean curvature (CMC) spheres in the homogeneous Riemannian 3-manifold Sol_3, i.e., the only Thurston 3-dimensional geometry where this problem remains open. Our main result states that, for…

In this paper we introduce the notion of contact angle for an immersed surface in three dimensional sphere. We deduce formulas for the Laplacian and for the Gaussian curvature, and we classify minimal surfaces in $S^3$ with constant contact…

We construct examples of compact and one-ended constant mean curvature surfaces with large mean curvature in Riemannian manifolds with axial symmetry by gluing together small spheres positioned end-to-end along a geodesic. Such surfaces…

We study Willmore surfaces of constant Moebius curvature $K$ in $S^4$. It is proved that such a surface in $S^3$ must be part of a minimal surface in $R^3$ or the Clifford torus. Another result in this paper is that an isotropic surface…

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…

Spacelike surfaces in the Lorentz-Minkowski space L^3 can be endowed with two different Riemannian metrics, the metric inherited from L^3 and the one induced by the Euclidean metric of R^3. It is well known that the only surfaces with zero…