Weak compactness of wave maps and harmonic maps

Relative Compactness and Product Stable Quotient Maps

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. §

Harmonic Maps and Biharmonic Maps

This is a survey on harmonic maps and biharmonic maps into (1) Riemannian manifolds of non-positive curvature, (2) compact Lie groups or (3) compact symmetric spaces, based mainly on my recent works on these topics.

relative compactness and product stable quotient maps

Stable Exponentially Harmonic Maps Between Finsler Manifolds