Extension of Lipschitz maps into 3-manifolds. (English) Zbl 1020.53024

Buyalo, Sergei; Schroeder, Viktor

Asian J. Math. 5, No. 4, 685-704 (2001).

The authors prove the following Lipschitz extension property for an arbitrary universal covering \(Y\) of a closed 3-dimensional manifold. Let \(S\) be some subset of an arbitrary metric space \(X\), and \(f:S\to Y\) be some \(\lambda\)-Lipschitz map. Then the map \(f\) can be extended to some \(c\lambda\)-Lipschitz map \(\bar f:X\to Y\) where the constant \(c\) does not depend on \(f\).

Reviewer: Valery Borisovich Marenich (Kalmar)

MSC:

53C23

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces

Keywords:

universal covering; closed 3-dimensional manifold; Lipschitz map