Distribution of triangles in sets of a given Hausdorff dimension and application to geometric combinatorics
Prof. Alex IosevichUniversity of Rochester 下午 2:30–4:00 Hongjing Hall 107 室Abstract:
We shall prove that of the Hausdorff dimension of a planar set is $>\frac{8}{5}$, then the three dimensional Lebesgue measure of the set of non-congruent triangles determined by $E$ is positive. Applications to geometric incidence theorems will be given.