Bezdek, Károly and Naszódi, Márton (2018) The Kneser–Poulsen Conjecture for Special Contractions. DISCRETE AND COMPUTATIONAL GEOMETRY, 60 (4). pp. 967-980. ISSN 0179-5376
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Abstract
The Kneser–Poulsen conjecture states that if the centers of a family of N unit balls in (Formula presented.) 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 (Formula presented.). 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. © 2018 Springer Science+Business Media, LLC, part of Springer Nature
| Item Type: | Article |
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| Additional Information: | N1 Article in Press Funding Agency and Grant Number: Natural Sciences and Engineering Research Council of Canada; National Research, Development and Innovation Office (NKFIH) [NKFI-K119670, NKFI-PD104744]; Hungarian Academy of Sciences; Ministry of Human Capacities [UNKP-17-4]; Swiss National Science Foundation [200020-162884, 200021-165977]\n Funding text: We thank Peter Pivovarov and Ferenc Fodor for our discussions. Karoly Bezdek was partially supported by a Natural Sciences and Engineering Research Council of Canada Discovery Grant. Marton Naszodi was partially supported by the National Research, Development and Innovation Office (NKFIH) grants: NKFI-K119670 and NKFI-PD104744 and by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences, as well as the UNKP-17-4 New National Excellence Program of the Ministry of Human Capacities. Part of his research was carried out during a stay at EPFL, Lausanne at Janos Pach's Chair of Discrete and Computational Geometry supported by the Swiss National Science Foundation Grants 200020-162884 and 200021-165977.\n |
| Uncontrolled Keywords: | VOLUME; PLANE; Kneser-Poulsen conjecture; Blaschke-Santaló inequality; Computer Science, Theory & Methods; Alexander's contraction; Ball-polyhedra; Volume of intersections of balls; Volume of unions of balls; 52A20; BALL-POLYHEDRA; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 22 Sep 2019 16:30 |
| Last Modified: | 22 Sep 2019 16:30 |
| URI: | http://real.mtak.hu/id/eprint/100302 |
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