Compactness properties of weakly p-harmonic maps into homogeneous spaces

Homotopy Classification of Maps into Homogeneous Spaces

We give an alternative to Postnikov’s homotopy classification of maps from 3-dimensional CW-complexes to homogeneous spaces G/H of Lie groups. It describes homotopy classes in terms of lifts to the group G and is suitable for extending the notion of homotopy to Sobolev maps. This is required in applications to variational problems of mathematical physics.

compactness theorem of n - harmonic maps

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. §

Jiang-type Theorems for Coincidences of Maps into Homogeneous Spaces

Let f, g : X → G/K be maps from a closed connected orientable manifold X to an orientable coset space M = G/K where G is a compact connected Lie group, K a closed subgroup and dimX = dimM . In this paper, we show that if L(f, g) = 0 then N(f, g) = 0; if L(f, g) 6= 0 then N(f, g) = R(f, g) where L(f, g), N(f, g), and R(f, g) denote the Lefschetz, Nielsen, and Reidemeister coincidence numbers of ...

Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces

The story begins with the paper of Müller, [59], who — for the sake of an application to nonlinear elasticity — proved that if the Jacobian determinant Ju of a Sobolev map u ∈ W 1,n loc (Rn ,Rn ) is nonnegative, then it belongs locally to L log L. The result is quite intriguing, since a priori Hölder inequality implies only that Ju ∈ L1 and one does not suspect any higher integrability. If one ...

Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces