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.
@article{bwmeta1.element.bwnjournal-article-bcpv50z1p267bwm,
author = {Siersma, Dirk},
title = {Properties of Conflict Sets in the Plane},
journal = {Banach Center Publications},
volume = {50},
year = {1999},
pages = {267-276},
zbl = {0959.53003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv50z1p267bwm}
}
Siersma, Dirk. Properties of Conflict Sets in the Plane. Banach Center Publications, Tome 50 (1999) pp. 267-276. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv50z1p267bwm/
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