In this paper, we prove the existence of nonconstant bounded harmonic maps on a Cartan-Hadamard manifold of pinched negative curvature by solving the asymptotic Dirichlet problem. To be precise, given any continuous data f on the boundary at infinity with image within a ball in the normal range, we prove that there exists a unique harmonic map from the manifold into the ball with boundary value f.
|Number of pages||11|
|Journal||Journal of the Korean Mathematical Society|
|State||Published - May 2005|
- Asymptotic Dirichlet Problem
- Harmonic maps