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math.MG2004
Separated sets and the Falconer conjecture for polygonal norms
Sergei Konyagin, Izabella Laba
The Falconer conjecture asserts that if E is a planar set with Hausdorff dimension strictly greater than 1, then its Euclidean distance set has positive one-dimensional Lebesgue me…
math.CO2004
Distance sets of well-distributed planar sets for polygonal norms
Sergei Konyagin, Izabella Laba
Let X be a 2-dimensional normed space, and let BX be the unit ball in X. We discuss the question of how large the set of extremal points of BX must be if X contains a well-distribu…