A bilinear Fourier extension theorem and applications to the distance set problem

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On the dimension of divergence sets of dispersive equations (2011, result): “In higher dimensions, combining the partial results due to Mattila [17], Sjolin [25,27], and Erdo˜gan [ 12 ], it is known that”
An L2-identity and pinned distance problem (2018, background): “)) ≥ CǫN1−ǫ. Unlike the Erd˝os distance problem, the Falconer distance conjecture is, however, far from being solved. The best currently known results are due to Wolﬀ ([25]) in the plane and Erdogan ([6]) in higher dimensions. They proved that ∆(E) has positive Lebesgue measure whenever dimH(E) >”
Weighted restriction estimates and application to Falconer distance set problem (2018, background): “The proof is essentially contained in Wolff [27] and Erdo˘gan [7].”
Erdös distance problem in vector spaces over finite fields (2005, background): “The best currently known result is due to Erdog̃an ([4]) and Wolff ([23]) who proved that the Lebesgue measure of the distance set is positive provided that the Hausdorff dimension of the set exceeds d2 + 1 3 .”