论文信息 - Algebraic methods in discrete analogs of the Kakeya problem

Algebraic methods in discrete analogs of the Kakeya problem

Abstract We prove the joints conjecture, showing that for any N lines in R 3 , there are at most O ( N 3 2 ) points at which 3 lines intersect non-coplanarly. We also prove a conjecture of Bourgain showing that given N 2 lines in R 3 so that no N lines lie in the same plane and so that each line intersects a set P of points in at least N points then the cardinality of the set of points is Ω ( N 3 ) . Both our proofs are adaptations of Dvir's argument for the finite field Kakeya problem.

Larry Guth | Nets Hawk Katz | L. Guth | N. Katz

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