We prove that every lambda -Lipschitz map f: S --> Y defined on a subset of
an arbitrary metric space X possesses a c lambda -Lipschitz extension (f)
over bar: X --> Y for some c = c(Y) greater than or equal to 1, provided Y
is a Hadamard manifold which satisfies one of the following conditions: (i)
Y has pinched negative sectional curvature, (ii) Y is homogeneous, (iii) Y
is two-dimensional. In case (i) the constant c depends only on the dimensi
on of Y and the pinching constant, in case (iii) one may take c := 4 root2.
We obtain similar results for large classes of Hadamard spaces Y in the se
nse of Alexandrov.