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math.CO2014★ 5 cited
Polynomials with dense zero sets and discrete models of the Kakeya conjecture and the Furstenberg set problem
Ruixiang Zhang
We prove the discrete analogue of Kakeya conjecture over . This result suggests that a (hypothetically) low dimensional Kakeya set cannot be constructed directly from…
math.CO2013★ 3 cited
On configurations where the Loomis-Whitney inequality is nearly sharp and applications to the Furstenberg set problem
Ruixiang Zhang
In this paper, we consider the so-called "Furstenberg set problem" in high dimensions. First, following Wolff's work on the two dimensional real case, we provide "reasonable" upper…