Paper Info
Title
Balanced Convex Partitions of Measures in R2
Abstract
Let n greater than or equal to 2 be an integer and let mu(1) and mu(2) be measures in R-2 such that each mu(i) is absolutely continuous with respect to the Lebesgue measure and mu(1) (R-2) = mu(2) (R-2) = n. Let u not equal 0 be a vector on the plane. We show that if mu(1) (B) = mu(2) (B) = n for some bounded domain B, then there exist positive integers n(1), n(2) with n(1) + n(2) = n and disjoint open half-planes D-1, D-2 such that D-1 boolean OR D-2 = R-2, mu(1) (D-1) = mu2(D2) = n(1) and mu(1) (D-2) = mu(2)(D-2) = n(2); or there exist positive integers n(1), n(2), n(3) with n(1) + n(2) + n(3) = n and disjoint open convex domains D-1, D-2, D-3 such that D-1 boolean OR D-2 boolean OR D-3 = R-2, mu(1)(D-1)= mu(2)(D-1)= n(1), mu(1), (D-2) = mu(2) (D-2) = n(2), mu(1) (D-3) = mu(2) (D-3) = n(3) and such that the ray D-1 boolean AND D-2 is parallel to u. We also show a similar result for partitioning of point sets on the plane.
Year
DOI
Venue
2002
10.1007/s003730200011
GRAPHS AND COMBINATORICS
DocType
Volume
Issue
Journal
18
1.0
ISSN
Citations 
PageRank 
0911-0119
7
0.75
References 
Authors
0
1
Name
Order
Citations
PageRank
Toshinori Sakai1549.64