Short communications

On the length of the set of extreme points for self-similar sets in $\mathbb R^2$

A. V. Tetenov

Gorno-Altaisk State University

Abstract: We proof that the set of extreme points of the convex hull of any self-similar set in $\mathbb R^2$ has zero $1$-dimensional Lebesgue measure.

Keywords: self-similar sets, fractal, convex hull, extreme points, Hausdorff measure.

UDC: 514.8, 515.12

MSC: 28A80

Received December 11, 2009, published December 12, 2009

Language: English

Bibliographic databases:

•