Related papers: Continuous deformations of harmonic maps and their…

To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation complexes by an…

This study explores the relationship between hypergraph automorphisms and the spectral properties of matrices associated with hypergraphs. For an automorphism $f$, an \( f \)-compatible matrices capture aspects of the symmetry, represented…

We continue our study, initiated in our earlier paper, of Riemann surfaces with constant curvature and isolated conic singularities. Using the machinery developed in that earlier paper of extended configuration families of simple divisors,…

Let $U$ be a multiply connected domain of the Riemann sphere $\hat{C}$ whose complement $\hat{C}\setminus U$ has $N<\infty$ components. We show that every conformal map on $U$ can be written as a composition of $N$ maps conformal on simply…

Explicit harmonic and wave maps are typically available only in highly symmetric or constant-curvature settings, where additional symmetry or integrability structures are present. We develop a reduction framework for pseudo-Riemannian…

We study an infinite family of one-parameter deformations, so-called $\alpha$-continued fractions, of interval maps associated to distinct triangle Fuchsian groups. In general for such one-parameter deformations, the function giving the…

Any deformation of a Weyl or Clifford algebra A can be realized through a `deforming map', i.e. a formal change of generators in A. This is true in particular if A is covariant under a Lie algebra g and its deformation is induced by some…

The infinite-dimensional unitary group U(infinity) is the inductive limit of growing compact unitary groups U(N). In this paper we solve a problem of harmonic analysis on U(infinity) stated in the previous paper math/0109193. The problem…

We investigate the existence of weak expanding solutions of the harmonic map flow for maps with values into a smooth closed Riemannian manifold. We prove the existence of such solutions in case the target manifold is isometrically embedded…

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…

In this paper we investigate the space of harmonic maps from a 2-torus to $\mathbb{S}^3$ using the spectral curve correspondence and Whitham deformations. In an open and dense subset of a parameter space we find that the space of harmonic…

We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to…

We investigate the geometry of the matrix model associated with an N=1 super Yang-Mills theory with three adjoint fields, which is a massive deformation of N=4. We study in particular the Riemann surface underlying solutions with arbitrary…

We study metric perturbations and deformation theory for degenerate Z/2-harmonic 1-forms. For a natural class of degenerate examples, we prove that after a suitable perturbation of the ambient Riemannian metric, the form can be deformed to…

Let $f$ be a harmonic map from a Riemann surface to a Riemannian $n$-manifold. We prove that if there is a holomorphic diffeomorphism $h$ between open subsets of the surface such that $f\circ h = f$, then $f$ factors through a holomorphic…

Many mathematicians encounter k-to-1 maps only in the study of covering maps. But, of course, k-to-1 maps do not have to be open. This paper touches on covering maps, and simple maps, but concentrates on ordinary k-to-1 functions (both…

We prove that the standard half-harmonic map $U:\mathbb{R}\to\mathbb{S}^1$ defined by \begin{equation*} x\to \begin{pmatrix} \frac{x^2-1}{x^2+1} \frac{-2x}{x^2+1} \end{pmatrix} \end{equation*} is nondegenerate in the sense that all bounded…

It is proved some results about existence and non existence of unit normal sections of submanifolds of the Euclidean space and sphere which associated Gauss maps are harmonic. Some applications to CMC hypersurfaces of the sphere and…

Pluriharmonic maps form an important class of harmonic maps which includes holomorphic maps. We study their morphisms, in particular the inter-relationships between $(1,1)$-geodesic, pluriharmonic and $\pm$holomorphic maps. Then we…

We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…