3 problems

Let $f$ satisfy Assumptions,, and, and let $D\subset\mathbb{R}^2$ be an open rectangle centred at the origin. Write $D_R$ for its dilation by $R$, and let $N_\mathrm{ES}(D_R,\ell)$…

Peakedness conjecture. Within the allowable range of exponents,

Abscissa generic level sets. A full Lebesgue measure set of abscissa points $x\in[0,1]$ have level sets $L(\tau(x))$ that are uncountable and have Hausdorff dimension $0$.