5 problems

Cone-and-cylinder Fourier-dimension conjecture. Then

A hypersurface $M$ in Euclidean space has principal curvatures, the eigenvalues of its Weingarten map, at each point. Its Fourier dimension, denoted by $\dim_F(M)$, measures the st…

Let $p>2$ be a prime number and let $\epsilon\in(0,1)$. Uniform Fourier-dimension conjecture. For every digit set $D$ with … we have … where the $o(1)$ term is uniform across all s…

Let $d$ be a positive integer, let $RY=\{ry:r\in R,\ y\in Y\}$ for $R\subseteq(0,\infty)$ and $Y\subseteq\mathbb{R}^d$. Dual fractal-set conjecture. For every $\alpha\in[0,1]$, the…

Let $d$ be a positive integer, let $\beta\beta\in[0,d]$, and let $RY=\{ry:r\in R,\ y\in Y\}$ for $R\subseteq(0,\infty)$ and $Y\subseteq\mathbb{R}^d$. Fractal-set conjecture. For ev…