Abstract for Rigidity Paper

Let X = G/K be a symmetric space where G is one of the classical noncompact Lie groups, e.g., SL(n,R) or SO(p,q). Let N be a smooth, compact discrete quotient of X, and let M be a Kahler manifold. We bound the dimension of the image of a harmonic map from M to N. This maximum dimension is usually the dimension of the largest hermitian symmetric space contained in X.