Kneser-Poulsen conjecture for a small number of intersections
نویسنده
چکیده
The Kneser-Poulsen conjecture says that if a finite collection of balls in the Euclidean space E is rearranged so that the distance between each pair of centers does not get smaller, then the volume of the union of these balls also does not get smaller. In this paper, we prove that if in the initial configuration the intersection of any two balls has common points with no more than d+1 other balls, then the conjecture holds.
منابع مشابه
M ar 2 00 9 From the Kneser - Poulsen conjecture to ball - polyhedra ∗
A very fundamental geometric problem on finite systems of spheres was independently phrased by Kneser (1955) and Poulsen (1954). According to their well-known conjecture if a finite set of balls in Eu-clidean space is repositioned so that the distance between the centers of every pair of balls is decreased, then the volume of the union (resp., intersection) of the balls is decreased (resp., inc...
متن کاملFrom the Kneser-Poulsen conjecture to ball-polyhedra
A very fundamental geometric problem on finite systems of spheres was independently phrased by Kneser (1955) and Poulsen (1954). According to their well-known conjecture if a finite set of balls in Euclidean space is repositioned so that the distance between the centers of every pair of balls is decreased, then the volume of the union (resp., intersection) of the balls is decreased (resp., incr...
متن کاملOn the weighted Kneser-Poulsen conjecture
Suppose that p = (p1,p2, . . . ,pN ) and q = (q1,q2, . . . ,qN ) are two configurations in Ed, which are centers of balls B(pi, ri) and B(qi, ri) of radius ri, for i = 1, . . . , N . In [9] it was conjectured that if the pairwise distances between ball centers p are contracted in going to the centers q, then the volume of the union of the balls does not increase. For d = 2 this was proved in [1...
متن کاملKneser-Poulsen conjecture for large radii
In this paper we prove the Kneser-Poulsen conjecture for large radii. Namely, if a finite number of points in Euclidean space En is rearranged so that the distance between each pair of points does not decrease, then there exists a positive number r0 that depends on the rearrangement of the points, such that if we consider ndimensional balls of radius r > r0 with centers at these points, then th...
متن کاملThe Kneser-Poulsen Conjecture for Spherical Polytopes
If a finite set of balls of radius π/2 (hemispheres) in the unit sphere Sn is rearranged so that the distance between each pair of centers does not decrease, then the (spherical) volume of the intersection does not increase, and the (spherical) volume of the union does not decrease. This result is a spherical analog to a conjecture by Kneser (1954) and Poulsen (1955) in the case when the radii ...
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عنوان ژورنال:
- Contributions to Discrete Mathematics
دوره 9 شماره
صفحات -
تاریخ انتشار 2014