Properties of Conflict Sets in the Plane
Volume 50 / 1999
Banach Center Publications 50 (1999), 267-276
DOI: 10.4064/-50-1-267-276
Abstract
This paper studies the smoothness and the curvature of conflict sets of the distance function in the plane. Conflict sets are also well known as 'bisectors'. We prove smoothness in the case of two convex sets and give a formula for the curvature. We generalize moreover to weighted distance functions, the so-called Johnson-Mehl model.