Related papers: Tori Embedded in S3 with Dense Asymptotic Lines

The classification of structurable tori with nontrivial involution, which was begun by Allison and Yoshii, is completed. New examples of structurable tori are obtained using a construction of structurable algebras from a semilinear version…

We continue to investigate some classes of Szeg\"o type polynomials in several variables. We focus on asymptotic properties of these polynomials and we extend several classical results of G. Szeg\"o to this setting.

The shape invariant of a symplectic manifold encodes the possible area classes of embedded Lagrangian tori. Potentially this is a powerful invariant, but for most manifolds the shape is unknown. We compute the shape for 4 dimensional…

We give a complete coarse classification of Legendrian and transverse torus knots in any contact structure on $S^3$.

We construct monotone Lagrangian tori in the standard symplectic vector space, in the complex projective space and in products of spheres. We explain how to classify these Lagrangian tori up to symplectomorphism and Hamiltonian isotopy, and…

We have studied the transport properties of LaTiO3/SrTiO3 (LTO/STO) heterostructures. In spite of 2D growth observed in reflection high energy electron diffraction, Transmission Electron Microscopy images revealed that the samples tend to…

Very recently Ben Andrews and Haizhong Li showed that every embedded cmc torus in the three dimensional sphere is axially symmetric. There is a two-parametric family of axially symmetric cmc surfaces; more precisely, for every real number H…

In this paper we give new existence results for complete non-orientable minimal surfaces in $\mathbb{R}^3$ with prescribed topology and asymptotic behavior.

We prove that 3-dimensional ellipsoids invariant under a 2-torus action contain infinitely many distinct immersed minimal tori, with at most one exception. These minimal tori bifurcate from the 2-torus orbit of largest volume at a dense set…

We classify the real tight contact structures on solid tori up to equivariant contact isotopy and apply the results to the classification of real tight structures on $S^3$ and real lens spaces $L(p,\pm 1)$. We prove that there is a unique…

The deformation problem for a transversely isotropic elastic layer bonded to a rigid substrate and coated with a very thin elastic layer made of another transversely isotropic material is considered. The leading-order asymptotic models (for…

We show that if a Jordan curve C in the asymptotic sphere contains a smooth point, there is an embedded H-plane in H^3 asymptotic to C for any H in [0,1).

We characterize all groups which can occur as the topological symmetry group or the orientation preserving topological symmetry group of some embedding of the Petersen graph in S^3.

Let E(1)_K denote the closed 4-manifold that is homotopy equivalent (hence homeomorphic) to the rational elliptic surface E(1) and is obtained by performing Fintushel-Stern knot surgery on E(1) using a knot K in S^3. We construct an…

Consider a Hodge manifold and assume that a torus acts on it in a Hamiltonian and holomorphic manner and that this action linearizes on a given quantizing line bundle. Inside the dual of the line bundle one can define the circle bundle,…

For applications in computing, Bezier curves are pervasive and are defined by a piecewise linear curve L which is embedded in R^3 and yields a smooth polynomial curve C embedded in R^3. It is of interest to understand when L and C have the…

We show that any grafting ray in Teichm\"{u}ller space determined by an arational lamination or a multi-curve is (strongly) asymptotic to a Teichm\"{u}ller geodesic ray. As a consequence the projection of a generic grafting ray to moduli…

We survey what is known about minimal surfaces in $\bold R^3 $ that are complete, embedded, and have finite total curvature. The only classically known examples of such surfaces were the plane and the catenoid. The discovery by Costa, early…

A Euclidean minimal torus with planar ends gives rise to an immersed Willmore torus in the conformal 3--sphere $S^3=\R^3\cup \{\infty\}$. The class of Willmore tori obtained this way is given a spectral theoretic characterization as the…

We consider circle patterns on closed tori equipped with complex projective structures. There is an embedding of the space of circle patterns to the Teichm\"{u}ller space of a punctured surface. Via the embedding, the Weil-Petersson…