# Extension of Lipschitz maps into 3-manifolds

Buyalo, S; Schroeder, V (2001). Extension of Lipschitz maps into 3-manifolds. Asian Journal of Mathematics, 5(4):685-704.

## Abstract

We prove that the universal covering Y of a closed nonpositively curved 3-dimensional Riemannian manifold possesses the following Lipschitz extension property: there exists a constant c ≥ 1 such that every λ-Lipschitz map f : S → Y defined on s subset S of an arbitrary metric space X has a cλ-Lipschitz extension f¯ : X → Y.

We prove that the universal covering Y of a closed nonpositively curved 3-dimensional Riemannian manifold possesses the following Lipschitz extension property: there exists a constant c ≥ 1 such that every λ-Lipschitz map f : S → Y defined on s subset S of an arbitrary metric space X has a cλ-Lipschitz extension f¯ : X → Y.