Name
Abstract | ||
|---|---|---|
The Kneser–Poulsen conjecture states that if the centers of a family of N unit balls in \({\mathbb E}^d\) are contracted, then the volume of the union (resp., intersection) does not increase (resp., decrease). We consider two types of special contractions. First, a uniform contraction is a contraction where all the pairwise distances in the first set of centers are larger than all the pairwise distances in the second set of centers. We obtain that a uniform contraction of the centers does not decrease the volume of the intersection of the balls, provided that \(N\ge (1+\sqrt{2})^d\). Our result extends to intrinsic volumes. We prove a similar result concerning the volume of the union. Second, a strong contraction is a contraction in each coordinate. We show that the conjecture holds for strong contractions. In fact, the result extends to arbitrary unconditional bodies in the place of balls. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s00454-018-9976-1 | Discrete & Computational Geometry |
Keywords | Field | DocType |
Kneser–Poulsen conjecture, Alexander’s contraction, Ball-polyhedra, Volume of intersections of balls, Volume of unions of balls, Blaschke–Santalo inequality, 52A20, 52A22 | Topology,Combinatorics,Ball (bearing),Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
60 | 4 | Discrete Comput. Geom. 60/4 (2018) 967-980 |
Citations | PageRank | References |
1 | 0.40 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Károly Bezdek | 1 | 39 | 14.90 |
| Marton Naszodi | 2 | 21 | 7.87 |