Related papers: Minimal partitions for anisotropic tori

We study square-tiled tori, that is, tori obtained from a finite collection of unit squares by parallel side identifications. Square-tiled tori can be parametrized in a natural way that allows to count the number of square-tiled tori tiled…

For various values of n, d, and the phase space dimension, we construct simple examples of Hamiltonian and reversible systems possessing smooth d-parameter families of invariant n-tori carrying conditionally periodic motions. In the…

We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization problems.

We prove that a system of coupled nonlinear Schr{\"o}dinger equations on the torus exhibits both stable and unstable small KAM tori. In particular the unstable tori are related to a beating phenomena which has been proved recently in [6].…

In this paper we discuss the relationship between a TRO $\mathcal{T}$ and a sub-TRO $\mathcal{S}$ that is the range of a TRO-conditional expectation on $\mathcal{T}$, a \textit{ternary corner}, by investigating a special class $\mathcal{D}$…

We show the existence of nontrivial stationary weak solutions to the surface quasi-geostrophic equations on the two dimensional periodic torus.

Nanotubes with proper thickness, size and texture make ultra-efficient sinks for the quantum particles traveling into specific background media. Several optimal semiconducting cylindrical layers are reported to achieve enhancement in the…

Chow, Li and Yi in [2] proved that the majority of the unperturbed tori {\it on sub-manifolds} will persist for standard Hamiltonian systems. Motivated by their work, in this paper, we study the persistence and tangent frequencies…

We construct embedded closed minimal surfaces in the round three-sphere, resembling two parallel copies of the Clifford torus, joined by m^2 small catenoidal bridges symmetrically arranged along a square lattice of points on the torus.

Minimal tori that are linearly full in the 3-sphere possess a natural invariant g called their spectral genus, which was introduced by Hitchin. We show that for each g>0, there are countably many real g-dimensional families of minimally…

We derive semiclassical quantization conditions for systems with spin. To this end one has to define the notion of integrability for the corresponding classical system which is given by a combination of the translational motion and…

We classify spin structures on the noncommutative torus, and find that the noncommutative n-torus has 2^n spin structures, corresponding to isospectral deformations of spin structures on the commutative n-torus. For n>3 the classification…

Local minimizers for the anisotropic isoperimetric problem in the small-volume regime on closed Riemannian manifolds are shown to be geodesically convex and small smooth perturbations of tangent Wulff shapes, quantitatively in terms of the…

Context. One of the often discussed models for X-ray binaries high-frequency quasi-periodic oscillations is the oscillating torus model that considers oscillation modes of slender accretion tori. Aims. Here, we aim at developing this model…

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…

Considered is quantum tunnelling in anisotropic spin systems in a magnetic field perpendicular to the anisotropy axis. In the domain of small field the problem of calculating tunnelling splitting of energy levels is reduced to constructing…

Starting from the product of a $3$-torus and a compact K\"ahler (respectively, hyperK\"ahler) manifold we construct via mapping tori generalized K\"ahler manifolds of split (respectively, non-split) type. In this way we obtain new…

In this survey, we review the properties of minimal spectral $k$-partitions in the two-dimensional case and revisit their connections with Pleijel's Theorem. We focus on the large $k$ problem (and the hexagonal conjecture) in connection…

H-minimal Lagrangian submanifolds in general K\"{a}hler manifolds generalize special Lagrangian submanifolds in Calabi-Yau manifolds. In this paper we will use the deformation theory of H-minimal Lagrangian submanifolds in K\"{a}hler…

We prove weak convergence of curvature tensors of Riemannian manifolds for converging noncollapsing sequences with a lower bound on sectional curvature.