Details

Autor(en) / Beteiligte

• Rataj, Jan
• Winter, Steffen

Titel

On Volume and Surface Area of Parallel Sets

Ist Teil von

• Indiana University mathematics journal, 2010-01, Vol.59 (5), p.1661-1685

Ort / Verlag

Bloomington, IN: Department of Mathematics of Indiana University

Erscheinungsjahr

2010

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The r-parallel set to a set A in a Euclidean space consists of all points with distance at most r from A. We clarify the relation between the volume and the surface area of parallel sets and study the asymptotic behaviour of both quantities as r tends to 0. We show, for instance, that in general, the existence of a (suitably rescaled) limit of the surface area implies the existence of the corresponding limit for the volume, known as the Minkowski content. A full characterisation is obtained for the case of self-similar fractal sets. Applications to stationary random sets are discussed as well, in particular, to the trajectory of the Brownian motion.