Ahlfors-Regular Curves In Metric Spaces

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We 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.
25 pages, No figures. revisions after referee comments. to appear in Annales Academae Scientiarum Fennicae Mathematica

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Metric Geometry, Classical Analysis and ODEs, 28A75

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http://salesiana.dossiersoluciones.com/handle/123456789/112829

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0605454
 http://arxiv.org/abs/math/0605454

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arXiv