The geometry of conflict sets

The purpose of this paper is to study the smoothness and curvature of confl‡ict sets of the distance function in the plane. In the fi…rst section part of the thesis,the fundamental concepts about Euclidean geometry and topology are given. In the second and the third parts of the thesis several important properties of con‡flict sets in the plane. Furthermore, some theorems about the smoothness and curvature of confl‡ict sets are proved. Finally, weighted distance function which is called Johnson-Mehl Model is shown. KEYWORDS : Conáict sets, Euclidean Space, Curvature