Open AccessRecent work connected with the Kakeya problem
Author(s) -
Thomas Wolff
Publication year - 2003
Publication title -
university lecture series
Language(s) - English
Resource type - Book series
eISSN - 2376-919X
pISSN - 1047-3998
DOI - 10.1090/ulect/029/11
Subject(s) - counterexample , set (abstract data type) , mathematics , measure (data warehouse) , metric (unit) , property (philosophy) , unit (ring theory) , work (physics) , discrete mathematics , computer science , engineering , operations management , epistemology , data mining , philosophy , mechanical engineering , mathematics education , programming language
where Sn−1 is the unit sphere in R. This paper will be mainly concerned with the following issue, which is still poorly understood: what metric restrictions does the property (1) put on the set E? The original Kakeya problem was essentially whether a Kakeya set as defined above must have positive measure, and as is well-known, a counterexample was given by Besicovitch in 1920. A current form of the problem is as follows:
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