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On volume vectors determined by hypergraphs in thin subsets of Euclidean space
Tainara Borges, Ben Foster, Yumeng Ou +2
Generalizing the Falconer distance problem, the authors of this paper recently established the first non-trivial dimensional threshold for any distance graph in high enough of a di…
Falconer-type results for any finite graph with multiple pins
Tainara Borges, Ben Foster, Yumeng Ou +2
A generalization of the celebrated Falconer distance problem asks for a graph , with vertex set and edge set , how large the…
Nonempty interior of pinned distance and tree sets
Tainara Borges, Benjamin Foster, Yumeng Ou +1
For a compact set , , consider the pinned distance set . Peres and Schlag showed that if the Hausdorff dimens…
Sobolev smoothing estimates for bilinear maximal operators with fractal dilation sets
Tainara Borges, Benjamin Foster, Yumeng Ou
Given a hypersurface , we study the bilinear averaging operator that averages a pair of functions over , as well as more general bilinear multipliers o…
Bounds for lacunary bilinear spherical and triangle maximal functions
Tainara Borges, Benjamin Foster
We prove bounds for certain lacunary bilinear maximal averaging operators with parameters satisfying the Hölder relation . The boundedne…
Sparse bounds for the bilinear spherical maximal function
Tainara Borges, Benjamin Foster, Yumeng Ou +2
We derive sparse bounds for the bilinear spherical maximal function in any dimension . When , this immediately recovers the sharp bound of…