Harmonic maps into metric spaces with curvature bounded above.

摘要

This dissertation deals with energy minimizing maps into metric spaces with curvature bounded above. Boundedness of the curvature of the target space is formulated in terms of triangle comparison. Several problems are solved. First the existence and uniqueness of the solution to the Dirichlet problem is established under the condition that the boundary data lie within a small geodesic ball. Next the interior and boundary regularity of that solution is proven. Finally it is shown that any minimizing map (no restrictions on its image) is regular if its energy is small enough.