On stable quasi-harmonic maps and Liouville type theorems

Liouville theorems for harmonic maps

Recently there has been much interest in the Liouville type theorems for harmonic maps. For a detailed survey and progress in this direction, see the works by Hildebrandt [4], Eells and Lemaire [2]. Here we would like to mention that for all known results, the conditions on the harmonic maps can be divided into two kinds. The first of these conditions concerns the finiteness of the energy of th...

Liouville Theorems for Dirac - Harmonic Maps

We prove Liouville theorems for Dirac-harmonic maps from the Euclidean space Rn, the hyperbolic space Hn and a Riemannian manifold Sn (n ≥ 3) with the Schwarzschild metric to any Riemannian manifold N .

Liouville-type theorems for stable and finite Morse index solutions of a quasi-linear elliptic equation

We establish Liouville-type theorems for stable and finite Morse index weak solutions of −∆pu = f(x)F (u) in R . For a general non-linearity F ∈ C(R) and f(x) = |x|, we prove such theorems in dimensions N ≤ 4(p+α) p−1 +p, for bounded radial stable solutions. Then, we give some point-wise estimates for not necessarily bounded solutions. Also, similar theorems will be proved for both radial finit...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

A Liouville theorem for harmonic maps and

A Liouville theorem is proved which generalizes the papers of Hu, MP].