Related papers: Monopoles and Harmonic Maps
We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.
Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold…
We study N=2 supersymmetric quantum mechanics of a charged particle on sphere in the background of Dirac magnetic monopole. We adopt CP(1) model approach in which the monopole interaction is free of singularity. In order to exploit manifest…
We define analytic maps between super Riemann surfaces which extend the notion of branched covering maps to a supersymmetric setting. We show that these super covering maps appear naturally both in symmetric product orbifolds of…
We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hypercomplex manifolds arising as limits of pluricomplex…
Gromov has shown how to construct holomorphic maps of the plane to a complex manifold with prescribed values on a lattice. In the present paper, a similar interpolation theorem for pseudo-holomorphic maps from the cylinder S to an…
In this paper, we review the progress in the analysis of magnetic monopoles as generalized states in quantum mechanics. We show that the considered model contains rich algebraic structure that generates symmetries which have been utilized…
Rational maps on the Riemann sphere occupy a distinguished niche in the general theory of smooth dynamical systems. First, rational maps are complex-analytic, so a broad spectrum of techniques can contribute to their study (quasiconformal…
Let $S$ be a punctured Riemann surface with Euler characteristic $\chi(S)<0$. For any unitary representation $\rho: \pi_1(S) \to U(N)$, we introduce its renormalized energy and its harmonic representatives, which are equivariant harmonic…
In this paper, we give complete classifications of linear $\infty$-harmonic maps between Euclidean and Heisenberg spaces, between Nil and Sol spaces. We also classify all $\infty$-harmonic linear endomorphisms of Sol space and show that…
We find the spectrum of magnetic monopoles produced in the symmetry breaking SU(5) to [SU(3)\times SU(2)\times U(1)']/Z_6 by constructing classical bound states of the fundamental monopoles. The spectrum of monopoles is found to correspond…
Magnetic monopoles in hyperbolic space are in correspondence with certain algebraic curves in mini-twistor space, known as spectral curves, which are in turn in correspondence with rational maps between Riemann spheres. Hyperbolic monopoles…
We extend the investigation of BPS saturated t'Hooft-Polyakov monopoles in $\mathcal{M}^{2}\times S^{2}$ to the general case of $SU(N)$ gauge symmetry. This geometry causes the resulting $N-1$ coupled non-linear ordinary differential…
We construct new explicit proper r-harmonic functions on the standard n-dimensional sphere S^n and hyperbolic space H^n for any r\ge 1 and n\ge 2.
We study the hypersymplectic geometry of the moduli space of solutions to Hitchin's harmonic map equations on a $G$-bundle. This is the split-signature analogue of Hitchin's Higgs bundle moduli space. Due to the lack of definiteness, this…
Hyperbolic monopole motion is studied for well separated monopoles. It is shown that the motion of a hyperbolic monopole in the presence of one or more fixed monopoles is equivalent to geodesic motion on a particular submanifold of the full…
These are expanded notes of lectures given at the Advanced Summer School on Modern Mathematical Physics (JINR Dubna, July 2005) and at the 8th International School-Seminar ``The actual problems of microworld physics 2005'' (Gomel-Dubna,…
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…
In this thesis we study dynamic of magnetic monopoles from Lagrangian density in Yang-Mills-Higgs field theory. In particular, we discuss BPS (Bogomolny Prasad Sommerfield) magnetic monopoles, described by SU(N) Bogomolny equations, which…
We prove that the space of dominant/non-constant holomorphic mappings from a product of hyperbolic Riemann surfaces of finite type into certain hyperbolic manifolds with universal cover a bounded domain is a finite set.