A. Both bi-harmonic map and f -harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study f -bi-harmonic maps as the critical points of the f -bi-energy functional 1 2 ∫ M f |τ(φ)| dvg. This class of maps generalizes both concepts of harmonic maps and biharmonic maps. We first derive the f -biharmonic map ...

Many topics in integrable surface geometry may be unified by application of the highly developed theory of harmonic maps of surfaces into (pseudo-)Riemannian symmetric spaces. On the one hand, such harmonic maps comprise an integrable system with spectral deformations, algebro-geometric solutions and dressing actions of loop groups generated by Bäcklund transforms [5], [6], [14], [21], [24]. On...

Harmonic mappings between two Riemannian manifolds is an object of extensive study, due to their wide applications in mathematics, science and engineering. Proving the existence of such mappings is challenging because of the non-linear nature of the corresponding partial differential equations. This thesis is an exposition of a theorem by Eells and Sampson, which states that any given map from ...

Introduction A map : M ! N of Riemannian manifolds is harmonic if it extremises the energy functional: Z jdj 2 dvol on every compact subdomain of M. Harmonic maps arise in many diierent contexts in Geometry and Physics (for an overview, see 15,16]) but the setting of concern to us is the following: take M to be 2-dimensional and N to be a Riemannian symmetric space of compact type. In this case...

For n ≥ 3, let Ω ⊂ R be a bounded smooth domain and N ⊂ R be a compact smooth Riemannian submanifold without boundary. Suppose that {un} ⊂ W (Ω, N) are weak solutions to the perturbed n-harmonic map equation (1.2), satisfying (1.3), and uk → u weakly in W (Ω, N). Then u is an n-harmonic map. In particular, the space of n-harmonic maps is sequentially compact for the weak-W 1,n topology. §

Following are the abstracts of contributions (i.e., talks and posters) to the 13th Annual Meeting of the IMS held at the National University of Ireland Maynooth, 6–8 September 2000. The abbreviations after the names designate: ‘M’ for main speaker, ‘S’ for speaker, ‘RS’ for research student, and ‘P’ for poster. The abstracts are included as provided by the contributors for this volume of the Bu...