On the 1/2 Problem of Besicovitch: quasi-arcs do not contain sharp saw-teeth.

Título inglés	On the 1/2 Problem of Besicovitch: quasi-arcs do not contain sharp saw-teeth.
Título español	Sobre el problema de 1/2 de Besicovitch: los cuasi arcos no contienen dientes de sierra pronunciados.
Autor/es	Farag, Hany M.
Organización	Dep. Math. California Inst. Technol., Pasadena CA, Estados Unidos
Revista	0213-2230
Publicación	2002, 18 (1): 17-40, 15 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	In this paper we give an alternative proof of our recent result that totally unrectifiable 1-sets which satisfy a measure-theoretic flatness condition at almost every point and sufficiently small scales, satisfy Besicovitch's 1/2-Conjecture which states that the lower spherical density for totally unrectifiable 1-sets should be bounded above by 1/2 at almost every point. This is in contrast to rectifiable 1-sets which actually possess a density equal to unity at almost every point. Our present method is simpler and is of independent interest since it mainly relies on general properties of finite sets of points satisfying a scale-invariant flatness condition. For instance it shows that a quasi-arc of small constant cannot contain sharp saw-teeth. (A)
Clasificación UNESCO	120217
Palabras clave español	Distancia de Hausdorff ; Conjuntos medibles ; Espacios métricos ; Rectificación
Código MathReviews	MR1924686
Código Z-Math	Zbl 1012.28003
Acceso al artículo completo