We study Dirac-harmonic maps from a Riemann surface to a sphere Sn. We show that a weakly Dirac-harmonic map is in fact smooth, and prove that the energy identity holds during the blow-up process.

We use simple methods from harmonic maps to investigate singularities of period mappings at infinity. More precisely, we derive a harmonic map version of Schmid’s nilpotent orbit theorem. MSC Classification 14M27, 58E20

Discretization of the harmonic map flow into spheres often uses a penalization or projection strategy, where the first suffers from the proper choice of an additional parameter, and the latter from the lack of a discrete energy law, and restrictive mesh-constraints. We propose an implicit scheme that preserves the sphere constraint at every node, enjoys a discrete energy law, and unconditionall...

It is shown that the usual first variational formula for the energy of a harmonic map (or equivariant harmonic map) with respect to the conformal structure on a two dimensional domain extends to case of nonpositively curved metric space targets. As applications, we recover Gardiner’s formula for the variation of the Hubbard-Masur differential and a proof of the existence and uniqueness of quadr...

Wavelet analysis as a p–adic harmonic analysis Abstract New orthonormal basis of eigenfunctions for the Vladimirov operator of p–adic fractional derivation is constructed. The map of p–adic numbers onto real numbers is considered. This map (for p = 2) provides an equivalence between the constructed basis of eigenfunctions of the Vladimirov operator and the wavelet basis in L 2 (R) generated fro...

Let f : M → G(m, n) be a harmonic map from surface into complex Grassmann manifold. In this paper, some sufficient conditions for the harmonic sequence generated by f to have degenerate ∂-transform or ∂-transform are given.

In this note, we provide an alternative proof of C-regularity of continuous weak solutions to the system of harmonic map or heat flow of harmonic maps by Riesz potential estimates between Morrey spaces.

Using three coupled harmonic oscillators, we propose a quantum approach without using qubits to efficiently factorize an integer with only three steps. These three harmonic oscillators are coupled together via nonlinear interactions. This factoring method can be applied even if two harmonic oscillators are prepared in mixed states. As simple examples, we show how to factorize N = 15 and 35 usin...

Selftrapping has been traditionally studied on the assumption that quasiparticles interact with harmonic phonons and that this interaction is linear in the displacement of the phonon. To complement recent semiclassical studies of anharmonicity and nonlinearity in this context, we present below a fully quantum mechanical analysis of a two-site system, where the oscillator is described by a tunab...

Recently, animations with deforming objects are frequently used in various Computer Graphics applications. Metamorphosis (or morphing) of three dimensional objects is one of techniques which realize a shape transformation between existing two or more objects. We present a new algorithm for 3D geometric metamorphosis between two objects based on Harmonic Map. Our algorithm is applicable for arbi...