9 problems

Finite-field radial projection exceptional-set conjecture.

Let $E\subset \mathbb{R}^d$ be a Borel set with $\dim_H(E)\in(k-1,k]$ for some $k\in\{0,1,\ldots,d-1\}$. Liu–Orponen's radial projection conjecture. … This strengthens the exceptio…

Let $E\subset \mathbb{R}^d$ be a Borel set, let $\dim_H(E)>d-1$, and let $s\leq d-1$ be a real number. Radial projection exceptional-set conjecture. … This conjecture strengthens t…

Let $X\subset\mathbb{R}^d$ be a Borel set, with $\operatorname{dim_H}(X)\leq d-1$, that is not contained in a hyperplane. For $y\in X$, let … be the radial projection of $X$ from…

Let $E$ and $F$ be Borel sets in the plane with $\dim_{\mathcal{H}}E>0$ and $\dim_{\mathcal{H}}F>0$, and suppose that $F$ is not contained in a line. For $y$ in the plane, let…

Orponen's conjecture.

Let $E\subset\mathbb{R}^d$ be a Borel set with $\dim_{\mathcal{H}} E\in(k-1,k]$, where $k=0,1,\dots,d-1$. For $y\in\mathbb{R}^d$, let $\pi^y(x)=(x-y)/|x-y|$ be the radial projectio…

Radial projection exceptional-set conjecture. One should have

Let $K\subset\mathbb{R}^{2}$ be a Borel set, not contained on a line, and define the set of unit vectors spanned by $K$ by … Here $\dim_{\mathrm{H}}$ denotes Hausdorff dimension. D…