Prof. Emo Welzl and Prof. Bernd Gärtner
|Mittagsseminar Talk Information|
Date and Time: Thursday, May 27, 2004, 12:15 pm
Duration: This information is not available in the database
Location: This information is not available in the database
Speaker: Pavel Valtr (Charles Univ., Prague)
We construct a (simply defined) strictly convex norm ||.|| in the plane such that for each n there is a set of n points determining Ω(n4/3) unit distances with respect to ||.||. This gives another evidence that a new proof technique will be needed to improve the currently best known upper bound O(n4/3) for Erdös' unit-distance problem in the euclidean plane. Our result is asymptotically best possible and disproves a conjecture of Brass. An analogous construction in R3 gives an almost tight lower bound Ω(n3/2). A connection to lattice problems and to geometric touching problems is also given.
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