Electronic Resource
Springer
Discrete & computational geometry
20 (1998), S. 499-514
ISSN:
1432-0444
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract. If disks are moved so that each center—center distance does not increase, must the area of their union also be nonincreasing? We show that the answer is yes, assuming that there is a continuous motion such that each center—center distance is a nonincreasing function of time. This generalizes a previous result on unit disks. Our proof relies on a recent construction of Edelsbrunner and on new isoperimetric inequalities of independent interest. We go on to show analogous results for the intersection and for holes between disks.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00009398
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