A notion of rectifiability modeled on Carnot groups
| dc.creator | Pauls, Scott D. | |
| dc.date | 2000-04-11 | |
| dc.date | 2004-07-13 | |
| dc.date.accessioned | 2026-07-07T04:34:42Z | |
| dc.date.available | 2026-07-07T04:34:42Z | |
| dc.description | We introduce a notion of rectifiability modeled on Carnot groups. Precisely, we say that a subset E of a Carnot group M and N is a subgroup of M, we say E is N-rectifiable if it is the Lipschitz image of a positive measure subset of N. First, we discuss the implications of N-rectifiability, where N is a Carnot group (not merely a subgroup of a Carnot group), which include N-approximability and the existence of approximate tangent cones isometric to N almost everywhere in E. Second, we prove that, under a stronger condition concerning the existence of approximate tangent cones isomorphic to N almost everywhere in a set E, that E is N-rectifiable. Third, we investigate the rectifiability properties of level sets of C^1_N functions, where N is a Carnot group. We show that for almost every real number t and almost every noncharacteristic point x in a level set of f, there exists a subgroup T_x of H and r >0 so that f^{-1}(t) intersected with B_H(x,r) is T_x-approximable at x and an approximate tangent cone isomorphic to T_x at x. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0004069 | |
| dc.identifier | http://arxiv.org/abs/math/0004069 | |
| dc.identifier | Indiana Univ. Math. J. 53 (2004), 49-82 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59008 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Differential Geometry | |
| dc.title | A notion of rectifiability modeled on Carnot groups | |
| dc.type | text |