Related papers: An atlas for tridiagonal isospectral manifolds

Observations suggest that our universe is spatially flat on the largest observable scales. Exactly six different compact orientable three-dimensional manifolds admit flat metrics. These six manifolds are therefore the most natural choices…

In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…

An oriented compact closed manifold is called inflexible if the set of mapping degrees ranging over all continuous self-maps is finite. Inflexible manifolds have become of importance in the theory of functorial semi-norms on homology.…

We construct a locally compact Hausdorff topology on the path space of a finitely aligned $k$-graph $\Lambda$. We identify the boundary-path space $\partial\Lambda$ as the spectrum of a commutative $C^*$-subalgebra $D_\Lambda$ of…

This paper describes new techniques for learning atlas-like representations of 3D surfaces, i.e. homeomorphic transformations from a 2D domain to surfaces. Compared to prior work, we propose two major contributions. First, instead of…

Let $\Gamma$ be a connected regular graph with an eigenvalue $\lambda$ and corresponding idempotent $E_{\lambda}$. Let ${\cal E}_{\lambda}=\langle J,E_{\lambda}\rangle^\circ$ be the algebra generated by $J$ and $E_\lambda$ with respect to…

For a compact, connected, oriented Riemannian $3$-manifold $(M, g)$ with smooth boundary $\partial M$, we explicitly give a local representation and a full symbol expression for the electromagnetic Dirichlet-to-Neumann map by factorizing…

We find the spectrum and eigenvectors of an arbitrary irreducible complex tridiagonal matrix with two-periodic main diagonal provided that the spectrum and eigenvectors of the matrix with the same sub- and superdiagonals and zero main…

We establish a correspondence between trisections of smooth, compact, oriented $4$--manifolds with connected boundary and diagrams describing these trisected $4$--manifolds. Such a diagram comes in the form of a compact, oriented surface…

We obtain the asymptotic distribution of eigenvalues of real symmetric tridiagonal matrices as their dimension increases to infinity and whose diagonal and off-diagonal elements asymptotically change with the index n as J_{nt+i nt+i}\sim…

We consider differentiable maps in the setting of Abstract Differential Geometry and we study the conditions that ensure the uniqueness of differentials in this setting. In particular, we prove that smooth maps between smooth manifolds…

We prove sharp criteria on the behavior of radial curvature for the existence of asymptotically flat or hyperbolic Riemannian manifolds with prescribed sets of eigenvalues embedded in the spectrum of the Laplacian. In particular, we…

The reduction of biharmonic maps equation in terms of the Maurer-Cartan form for all smooth map of any compact Riemannian manifolds into a compact Lie group with bi-invariant Riemannian metric is obtained. By this formula, all the…

We show that the first five of the axioms we had formulated on spectral triples suffice (in a slightly stronger form) to characterize the spectral triples associated to smooth compact manifolds. The algebra, which is assumed to be…

A relationship between the tetrahedron equation for maps and the consistency property of integrable discrete equations on $\mathbb{Z}^3$ is investigated. Our approach is a generalization of a method developed in the context of Yang-Baxter…

For a compact manifold, which has a part isometric to a cylinder of finite length, we consider an adiabatic limit procedure, in which the length of the cylinder tends to infinity. We study the asymptotic of the spectrum of Hodge-Laplacian…

This paper extends the results of the previous work of the authors on the classification on noncommutative domain algebras up to completely isometric isomorphism. Using Sunada's classification of Reinhardt domains in $C^n$, we show that…

We study the parameter space structure of degree $d \ge 3$ one complex variable polynomials as dynamical systems acting on $\C$. We introduce and study {\it straightening maps}. These maps are a natural higher degree generalization of the…

Let S be an nXn real symmetric matrix with spectral decomposition S=Q^T Lambda Q, where Q is an orthogonal matrix and Lambda is diagonal with simple spectrum {lambda_1,..., lambda_n}. Also let O_S e R_S be the orbits by conjugation of S by,…

We consider a family of compact, oriented and connected Riemannian manifolds shrinking to a metric graph and describe the asymptotic behaviour of the eigenvalues of the Hodge Laplacian. We apply our results to produce manifolds with…