Extensions of Lipschitz maps into Hadamard spaces

  title={Extensions of Lipschitz maps into Hadamard spaces
  author={Udo Lang and Budimir Pavlovi{\'c} and Valeska Schroeder},
  journal={Geometric & Functional Analysis GAFA},
Abstract. We prove that every $ \lambda $-Lipschitz map $ f : S \to Y $ defined on a subset of an arbitrary metric space X possesses a $ c \lambda $-Lipschitz extension $ \bar{f} : X \to Y $ for some $ c = c(Y) \ge 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 dimension of Y and the pinching constant, in… CONTINUE READING