Ahlfors-Regular Curves In Metric Spaces

Simple item page
dc.creatorSchul, Raanan
dc.date2006-05-16
dc.date2006-12-11
dc.date.accessioned2026-07-07T07:14:19Z
dc.date.available2026-07-07T07:14:19Z
dc.descriptionWe discuss 1-Ahlfors-regular connected sets in a general metric space and prove that such sets are `flat' on most scales and in most locations. Our result is quantitative, and when combined with work of I. Hahlomaa, gives a characterization of 1-Ahlfors regular subsets of 1-Ahlfors-regular curves in metric spaces. Our result is a generalization to the metric space setting of the Analyst's (Geometric) Traveling Salesman theorems of P. Jones, K. Okikiolu, and G. David and S. Semmes, and it can be stated in terms of average Menger curvature.
dc.description25 pages, No figures. revisions after referee comments. to appear in Annales Academae Scientiarum Fennicae Mathematica
dc.identifierhttps://arxiv.org/abs/math/0605454
dc.identifierhttp://arxiv.org/abs/math/0605454
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112829
dc.subjectMetric Geometry
dc.subjectClassical Analysis and ODEs
dc.subject28A75
dc.titleAhlfors-Regular Curves In Metric Spaces
dc.typetext

Files

Collections

arXiv