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.
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Received November 6, 1996, and in revised form June 16, 1997, and September 23, 1997.
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Bern, M., Sahai, A. Pushing Disks Together—The Continuous-Motion Case . Discrete Comput Geom 20, 499–514 (1998). https://doi.org/10.1007/PL00009398
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DOI: https://doi.org/10.1007/PL00009398