Related papers: Minimal surfaces in $S^3$ foliated by circles

In Euclidean space we study surfaces with constant anisotropic mean curvature $\Lambda$ of the Dirichlet energy $\int_\Omega( |Du|^2+\Lambda u)$. We prove the existence of non-rotational surfaces with $\Lambda=0$ and foliated by a…

We show that any noncompact oriented surface is homeomorphic to the leaf of a minimal foliation of a closed $3$-manifold. These foliations are (or are covered by) suspensions of continuous minimal actions of surface groups on the circle.…

Building on work of Kapouleas and Yang, we construct sequences of minimal surfaces embedded in the round 3-sphere which converge to the Clifford torus counted with multiplicity two and have second fundamental form blowing up at every point…

We show that the number of genus $g$ embedded minimal surfaces in $\mathbb{S}^3$ tends to infinity as $g\rightarrow\infty$. The surfaces we construct resemble doublings of the Clifford torus with curvature blowing up along torus knots as…

By work of Uhlenbeck, the largest principal curvature of any least area fiber of a hyperbolic $3$-manifold fibering over the circle is bounded below by one. We give a short argument to show that, along certain families of fibered hyperbolic…

We study framed surfaces, which are a class of Euclidean minimal and hyperbolic CMC-1 surfaces that generalize immersed minimal surfaces in $\mathbb{R}^3$ and Bryant surfaces. For this class we prove a lower bound on the (unrestricted)…

In this paper, we study trigonal minimal surfaces in flat tori. First, we show a topological obstruction similar to that of hyperelliptic minimal surfaces. Actually, the genus of trigonal minimal surface in 3-dimensional flat torus must be…

In this paper we characterize concircular helices in $R^3$ by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in $R^3$ as a special family of ruled surfaces, and we…

In (the surface of) a convex polytope P^3 in R^4, an area-minimizing surface avoids the vertices of P and crosses the edges orthogonally. In a smooth Riemannian manifold M with a group of isometries G, an area-minimizing G-invariant…

Singular Riemannian Foliations are particular types of foliations on Riemannian manifolds, in which leaves locally stay at a constant distance from each other. Singular Riemannian Foliations in round spheres play a special role, since they…

We present a general construction of embedded minimal and constant mean curvature surfaces in $\mathbb{S}^n$ and one-phase free boundaries joined by a smooth interpolation by capillary hypersurfaces. This framework recovers all known…

In this paper, we prove that if a quasi-Fuchsian 3-manifold contains a minimal surface whose principle curvature is less than 1, then it admits a foliation such that each leaf is a surface of constant mean curvature. The key method that we…

We show the existence of a local foliation of a three dimensional Riemannian manifold by critical points of the Willmore functional subject to a small area constraint around non-degenerate critical points of the scalar curvature. This…

In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R^3. By means of a…

For each integer m>1 and l>0 we construct a pair of compact embedded minimal surfaces of genus 1+4m(m-1)l. These surfaces desingularize the m Clifford tori meeting each other along a great circle at the angle of \pi/m. They are invariant…

We present a method to construct a large family of Lagrangian surfaces in complex Euclidean plane by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves,…

We define two transforms between minimal surfaces with non-circular ellipse of curvature in the 5-sphere, and show how this enables us to construct, from one such surface, a sequence of such surfaces. We also use the transforms to show how…

We classify ruled minimal surfaces in $\Bbb R^3$ with density $e^z.$ It is showed that there is no noncylindrical ruled minimal surface and there is a family of cylindrical ruled minimal surfaces in $\Bbb R^3$ with density $e^z.$ It is also…

In the present paper, a new type of ruled surfaces called osculating-type (OT)-ruled surface is introduced and studied. First, a new orthonormal frame is defined for OT-ruled surfaces. The Gaussian and the mean curvatures of these surfaces…

We study symmetric minimal surfaces in the three-dimensional Heisenberg group $\mathrm{Nil}_3$ using the generalized Weierstrass type representation, the so-called loop group method. In particular, we will discuss how to construct minimal…