Related papers: Harmonic, Holomorphic and Rational Maps from Self-…

Motivated by a class of near BPS Skyrme models introduced by Adam, S\'anchez-Guill\'en and Wereszczy\'nski, the following variant of the harmonic map problem is introduced: a map $\phi:(M,g)\rightarrow (N,h)$ between Riemannian manifolds is…

We generalize Cartan's logarithmic derivative of a smooth map from a manifold into a Lie group $G$ to smooth maps into a homogeneous space $M=G/H$, and determine the global monodromy obstruction to reconstructing such maps from…

Let G be a complex semisimple Lie group, K a maximal compact subgroup and V an irreducible representation of K. Denote by M the unique closed orbit of G in P(V) and by O its image via the moment map. For any measure on M we construct a map…

Let U be a real form of a complex semisimple Lie group, and tau, sigma, a pair of commuting involutions on U. This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and…

In this paper we consider approximations introduced by Sacks-Uhlenbeck of the harmonic energy for maps from $S^2$ into $S^2$. We continue the analysis in [6] about limits of $\alpha$-harmonic maps with uniformly bounded energy. Using a…

We study geodesics of the form $\gamma(t)=\pi(\exp(tX)\exp(tY))$, $X,Y\in \fr{g}=\operatorname{Lie}(G)$, in homogeneous spaces $G/K$, where $\pi:G\rightarrow G/K$ is the natural projection. These curves naturally generalise homogeneous…

The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system with a complex projective Hilbert space as its phase space, thus equipped with a Riemannian metric in addition to a symplectic structure.…

This paper is the third of a series on Hamiltonian stationary Lagrangian surfaces. We present here the most general theory, valid for any Hermitian symmetric target space. Using well-chosen moving frame formalism, we show that the equations…

For a harmonic map $u:M^3\to S^1$ on a closed, oriented $3$--manifold, we establish the identity $$2\pi \int_{\theta\in S^1}\chi(\Sigma_{\theta})\geq \frac{1}{2}\int_{\theta\in S^1}\int_{\Sigma_{\theta}}(|du|^{-2}|Hess(u)|^2+R_M)$$ relating…

We define the space of nearly holomorphic automorphic forms on a connected reductive group $G$ over $\mathbb{Q}$ such that the homogeneous space $G(\mathbb{R})^1/ K_\infty^\circ$ is a Hermitian symmetric space. By Pitale, Saha and Schmidt's…

Let X be a compact (resp. compact and nonsingular) real algebraic variety and let Y be a homogeneous space for some linear real algebraic group. We prove that a continuous (resp. C^infinity) map f:X-->Y can be approximated by regular maps…

We study a recently proposed modification of the Skyrme model that possesses an exact self-dual sector leading to an infinity of exact Skyrmion solutions with arbitrary topological (baryon) charge. The self-dual sector is made possible by…

We study proper rational maps from the unit disk to balls in higher dimensions. After gathering some known results, we study the moduli space of unitary equivalence classes of polynomial proper maps from the disk to a ball, and we establish…

Rational discrete cohomology and homology for a totally disconnected locally compact group $G$ is introduced and studied. The $\mathrm{Hom}$-$\otimes$ identities associated to the rational discrete bimodule $\mathrm{Bi}(G)$ allow to…

Satake has constructed compactifications of symmetric spaces D=G/K which (under a condition called geometric rationality by Casselman) yield compactifications of the corresponding locally symmetric spaces. The different compactifications…

We extend many known results for harmonic maps from the 2-sphere into a Grassmannian to harmonic maps of finite uniton number from an arbitrary Riemann surface. Our method relies on a new theory of nilpotent cycles arising from the diagrams…

In this paper we consider two generalizations of the Skyrme model. One is a variational problem for maps from a compact three-manifold to a compact Lie group. The other is a variational problem for flat connections. We describe the path…

We study the equivariant harmonic map heat flow, Schr\"odinger maps equation, and generalized Landau-Lifshitz equation from $\mathbb{C}^n$ to $\mathbb{C}\mathbb{P}^n$. By means of a careful geometric analysis, we determine a new, highly…

Let $F$ be a non-archimedean local field with residue field $\mathbb{F}_q$ and let $G = GL_{2/F}$. Let $\mathbf{q}$ be an indeterminate and let $H^{(1)}(\mathbf{q})$ be the generic pro-p Iwahori-Hecke algebra of the group $G(F)$. Let…

We consider postcritically finite rational maps $f\colon \widehat{\mathbb{C}} \to \widehat{\mathbb{C}}$ whose Julia set is the whole Riemann sphere $\widehat{\mathbb{C}}$. We call such a map an expanding rational Thurston map. Identifying…