3 problems

Benítez–Sarantopoulos–Tonge conjecture. One has

Let $v_1,\ldots,v_d$ and $x$ be vectors in $\mathbb{R}^d$, and let $\langle v_i,x\rangle$ denote their Euclidean inner product. Real linear polarization constant conjecture. … More…

Let $c_n(X)$ denote the $n$th linear polarization constant of a normed space $X$, and let ${\bf R}^n$ be the real Euclidean space. Révész–Sarantopoulos conjecture. … This conjectur…