The harmonic morphisms φ : M → Nn are studied using the methods of the moving frame and exterior differential systems and three main results are achieved. The first result is a local structure theorem for such maps in the case that φ is a submersion, in particular, a normal form is found for all such φ once the metric on the target manifold N is specified. The second result is a finiteness theo...

Surface harmonic map between genus-0 surfaces plays an important role in applied mathematics and engineering, with applications in medical imaging and computer graphics. Previous work [1] introduces a variational approach for computing surface harmonic maps. It obtains global conformal parameterizations of genus-0 surfaces through minimizing the harmonic energy. Two weaknesses of this approach ...

Bachmann, Takeyama and Tasaka introduced the Q-linear map ϕ on harmonic algebra H1, which we call symmetrization in this paper. They calculated ϕ(w) explicitly for an element w H1 related to multiple zeta values of Mordell–Tornheim type. In paper, introduce its t-adic generalization ϕˆ calculate ϕˆ(w) elements H1〚t〛 constructed from theory 2-colored rooted trees.

In this paper we consider perturbed harmonic map equations for maps between closed Riemannian manifolds. In the case where the target manifold has negative sectional curvature we prove among other results that for a large class of semilinear and quasilinear perturbations, the perturbed harmonic map equations have solutions in any homotopy class of maps for which the Euler characteristic of the ...

This paper addresses control of nonlinear harmonic coupling in a pulsed jet injection experiment using a repetitive based control strategy for periodic reference tracking. A data driven approach identifies the harmonic interaction around a particular operating condition and generates a model for controller analysis and design. The single-input, singleoutput nonlinear plant is modeled as a nonli...

where τ( f ) is the tension field of f and dvg is the volume form of M. It is clear that E2( f |Ω) = 0 on any compact domain if and only if f is a harmonic map. Thus E2 provides a measure for the extent to which f fails to be harmonic. If f is a critical point of (1.1) over every compact domain, then f is called a biharmonic map or 2-harmonic maps. Jiang [10] proved that f is biharmonic if and ...