相关论文: Harmonic Self-maps of $\mbox{SU}(3)$

We examine a family of 3-point mappings that include mappings solvable through linearization. The different origins of mappings of this type are examined: projective equations and Gambier systems. The integrable cases are obtained through…

We consider harmonic maps from Minkowski space into the three sphere. We are especially interested in solutions which are asymptotically constant, i.e. converge to the same value in all directions of spatial infinity. Physical 3-space can…

The purpose of this paper is to prove that the spectrum of the non-self-adjoint one-particle Hamiltonian proposed by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433--6443) has interior points. We do this by first recalling that the…

We prove that counting the analytic Brouwer degree of rational coefficient polynomial maps in $\operatorname{Map}(\mathbb C^d, \mathbb C^d)$ -- presented in degree-coefficient form -- is hard for the complexity class $\operatorname{\sharp…

We study the order of affine and linear invariant families of planar harmonic mappings in the unit disk and determine the order of the family of mappings with bounded Schwarzian norm. The result shows that finding the order of the class…

We study minimal harmonic maps $g: {\mathbb{C}} \to SO(3) \backslash SL(3,{\mathbb{R}})$, parameterized by polynomial cubic differentials $P$ in the plane. The asymptotic structure of such a $g$ is determined by a convex polygon $Y(P)$ in…

In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…

In this paper we give a positive answer to the open existence problem for complex-valued harmonic morphisms from the non-compact irreducible Riemannian symmetric spaces $SL_n(R)/SO(n)$, $SU^*(2n)/Sp(n)$ and their compact duals $SU(n)/SO(n)$…

We study a second order differential equation corresponding to rotationally symmetric $F$-harmonic maps between certain noncompact manifolds. We show unique continuation and Liouville's type theorems for positive solutions. Asymptotic…

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…

We study the class of selfless C*-probability spaces introduced by Robert. It is known that a selfless tracial algebra has strict comparison and a unique trace. We prove that for separable tracial C*-algebras, selflessness is equivalent to…

This is primarily a survey of the developments in the theory of harmonic maps of finite uniton number (or unitons) which have taken place since the introduction of extended solutions by Uhlenbeck. Such maps include all harmonic maps from…

This paper establishes new upper bounds for the sum of the $k$ largest eigenvalues of symmetric matrices. When applied to the adjacency matrix of a graph, our results improve upon a related bound due to Mohar {\bf [On the sum of k largest…

Two classes of infinite series involving harmonic numbers and the binomial coefficient $C(3n,n)$ are evaluated in closed form using integrals. Several remarkable integral values and difficult series identities are stated as special cases of…

Given a closed manifold of dimension at least three, with non trivial homotopy group \pi_3(M) and a generic metric, we prove that there is a finite collection of harmonic spheres with Morse index bound one, with sum of their energies…

We prove the existence of radial self-similar singular solutions for the mass supercritical Nonlinear Schr\"odinger Equation far from the critical regime and, more generally, branches of such solutions for the Complex Ginzburg-Landau…

The paper presents a first step towards a family index theorem for classical self-adjoint boundary value problems. We address here the simplest non-trivial case of manifolds with boundary, namely the case of two-dimensional manifolds. The…

Let $H_n =\sum\limits_{k=1}^n \frac{1}{k}$ be the $n$-th harmonic number. Euler extended it to complex arguments and defined $H_r$ for any complex number $r$ except for the negative integers. In this paper, we give a new proof of the…

We study the iterative behavior of the family of 3-step linear fractional recurrences and the family of birational maps they define. We determine all the possible periodicities within this family or, equivalently, the birational maps of…

The eigenfamilies of Gudmundsson and Sakovich can be used to generate harmonic morphisms, proper $r$-harmonic maps, and minimal co-dimension $2$ submanifolds. This article begins by characterising the globally defined eigenfamilies of the…