Related papers: 1+1 wave maps into symmetric spaces

We prove a Simons-type holonomy theorem for totally skew 1-forms with values in a Lie algebra of linear isometries. The only transitive case, for this theorem, is the full orthogonal group. We only use geometric methods and we do not use…

Mackey showed that for a compact Lie group $K$, the pair $(K,C^{0}(K))$ has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this result to the unitary equivalence of quantizations for an…

We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation…

In this paper, we continue our study of equivariant \emph{wave maps on a wormhole} initiated in our companion paper. More precisely, we study finite energy $\ell$--equivariant wave maps from the (1+3)-dimensional spacetime $\mathbb R \times…

We introduce a general framework for training flow matching models on Riemannian symmetric spaces, a large class of manifolds that includes the sphere, hyperbolic space and Grassmannians. We exploit their algebraic structure to reformulate…

The immersion of the string world sheet, regarded as a Riemann surface, in $R^3$ and $R^4$ is described by the generalized Gauss map. When the Gauss map is harmonic or equivalently for surfaces of constant mean curvature, we obtain…

The bi-Hamiltonian structure of the two known vector generalizations of the mKdV hierarchy of soliton equations is derived in a geometrical fashion from flows of non-stretching curves in Riemannian symmetric spaces G/SO(N). These spaces are…

We discuss the $(1+1)$-dimensional wave maps equation with values in a compact Lie group. The corresponding Gibbs measure is given by a Brownian motion on the Lie group, which plays a central role in stochastic geometry. Our main theorem is…

The quantization of Class A Bianchi Type VI and VII geometries -with all six scale factors, as well as the lapse function and the shift vector present- is considered. A first reduction of the initial 6-dimensional configuration space is…

We study compact locally homogeneous plane waves. Such a manifold is a quotient of a homogeneous plane wave $X$ by a discrete subgroup of its isometry group. This quotient is called standard if the discrete subgroup is contained in a…

We construct Lie algebras of vector fields on universal bundles $\mathcal{E}^2_{N,0}$ of symmetric squares of hyperelliptic curves of genus $g=1,2,\dots$, where $g=\left[\frac{N-1}{2}\right], \ N=3,4,\ldots$. For each of these Lie algebras,…

We study finite-time blowup for a nonlinear wave equation for maps from the Minkowski space $\mathbb{R}^{1+d}$ into the 1-sphere $\mathbb{S}^1$, whose nonlinearity exhibits a null-form structure. We construct, for every dimension $d \geq…

We study the ``hyperboloidal Cauchy problem'' for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behaviour at the boundary, or with polyhomogeneous initial data.…

In this paper we study $k$-equivariant wave maps from the hyperbolic plane into the $2$-sphere as well as the energy critical equivariant $SU(2)$ Yang-Mills problem on $4$-dimensional hyperbolic space. The latter problem bears many…

Let $\varphi\in C^0 \cap W^{1,2}(\Sigma, X)$ where $\Sigma$ is a compact Riemann surface, $X$ is a compact locally CAT(1) space, and $W^{1,2}(\Sigma,X)$ is defined as in Korevaar-Schoen. We use the technique of harmonic replacement to prove…

We present a B\"acklund transformation (a discrete symmetry transformation) for the self-duality equations for supersymmetric gauge theories in N-extended super-Minkowski space ${\cal M}^{4|4N}$ for an arbitrary semisimple gauge group. For…

This is the first part of a two-paper series that establishes the uniqueness and regularity of a threshold energy wave map that does not scatter in both time directions. Consider the two-sphere valued equivariant energy critical wave maps…

In this work, we consider a Shallow-Water Quasi Geostrophic equation on the sphere, as a model for global large-scale atmospheric dynamics. This equation, previously studied by Verkley (2009) and Schubert et al. (2009), possesses a rich…

We consider a Klein-Gordon equation (KG) on a Riemannian compact surface, for which the flow lets invariant the two dimensional space the solutions independent of the space variable. It turns out that in this invariant space, there is a…

This article describes the symmetries of plane wave spacetimes in dimension four and greater. It begins with a description of the isometric automorphisms, and in particular the homogeneous plane waves. Then the article turns to describing…