Metric Spaces with Linear Extensions Preserving Lipschitz Condition
| dc.creator | Brudnyi, A. | |
| dc.creator | Brudnyi, Yu. | |
| dc.date | 2004-04-17 | |
| dc.date | 2005-10-10 | |
| dc.date.accessioned | 2026-07-07T06:36:42Z | |
| dc.date.available | 2026-07-07T06:36:42Z | |
| dc.description | We study a new bi-Lipschitz invariant λ(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor controlled by λ(M). We prove that λ(M) is finite for several important classes of metric spaces. These include metric trees of arbitrary cardinality, groups of polynomial growth, Gromov-hyperbolic groups, certain classes of Riemannian manifolds of bounded geometry and finite direct sums of arbitrary combinations of these objects. On the other hand we construct an example of a two-dimensional Riemannian manifold M of bounded geometry for which λ(M)=\infty. | |
| dc.description | Several new results are added, some important estimates are improved | |
| dc.identifier | https://arxiv.org/abs/math/0404304 | |
| dc.identifier | http://arxiv.org/abs/math/0404304 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100172 | |
| dc.subject | Metric Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | 26B35; 54E35; 46B15 | |
| dc.title | Metric Spaces with Linear Extensions Preserving Lipschitz Condition | |
| dc.type | text |