Differentiating maps into L^1 and the geometry of BV functions
| dc.creator | Cheeger, Jeff | |
| dc.creator | Kleiner, Bruce | |
| dc.date | 2006-11-30 | |
| dc.date | 2006-12-12 | |
| dc.date.accessioned | 2026-07-07T06:36:06Z | |
| dc.date.available | 2026-07-07T06:36:06Z | |
| dc.description | This is one of a series of papers examining the interplay between differentiation theory for Lipschitz maps, X-->V, and bi-Lipschitz nonembeddability, where X is a metric measure space and V is a Banach space. Here, we consider the case V=L^1 where differentiability fails. We establish another kind of differentiability for certain X, including R^n and H, the Heisenberg group with its Carnot-Cartheodory metric. It follows that H does not bi-Lipschitz embed into L^1, as conjectured by J. Lee and A. Naor. When combined with their work, this provides a natural counter example to the Goemans-Linial conjecture in theoretical computer science; the first such counterexample was found by Khot-Vishnoi. A key ingredient in the proof of our main theorem is a new connection between Lipschitz maps to L^1 and functions of bounded variation, which permits us to exploit recent work on the structure of BV functions on the Heisenberg group. | |
| dc.identifier | https://arxiv.org/abs/math/0611954 | |
| dc.identifier | http://arxiv.org/abs/math/0611954 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99983 | |
| dc.subject | Metric Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | Group Theory | |
| dc.title | Differentiating maps into L^1 and the geometry of BV functions | |
| dc.type | text |