# On hinges inside thin subsets of Euclidean spaces

Date:
Thursday, 1 February, 2018 - 14:00 - 15:00
Venue:
LSB 219
Seminar Type:
Seminar
Speaker Name:
Dr. Bochen LIU
Affiliation:
Bar-Ilan University
Abstract:

In this talk we will show that when the Hausdorff dimension of a subset $E \subset \mathbb{R}^d$ is greater than $\frac{d}{2}+\frac{1}{3}$, the Lebesgue measure of $$\{(|x-y|, |y-z|):x,y,z\in E\}$$ must be positive. It can be seen as a progress from the distance problem, where $\frac{d}{2}+\frac{1}{3}$ is known, to the pinned distance problem, where $\frac{d}{2}+\frac{1}{3}$ is expected.

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