5 problems

For $k\geq1$, let $\Delta_k(\varepsilon)$ denote the function studied in the paper, with $0\leq\varepsilon\leq1$. Delta three and Delta four polygonal conjecture. The graph of…

Alvino–Ferone–Trombetti's conjecture. Every extremal function $u$ for inequality (1.1) is of the form

Let $\mathcal{A}_+(28)$ denote the class of radial Schwartz functions on $\mathbb{R}^{28}$ satisfying the positive Fourier-eigenfunction uncertainty conditions. Dimension-28 root-l…

Two-slope extremality conjecture. If the function has no uncovered components, then it is extreme.

Let $t$ be a nonnegative integer, and let $\mathit{fw}(u)$ denote the formation width of a sequence $u$. Formation width conjecture. … The paper states that this would imply nearly…