4 problems

For real $p\geq 1$, let $\ell_p^d$ be $\mathbb R^d$ equipped with the norm … and let $\ell_\infty^d$ use the norm $\|\mathbf x\|_\infty=\max_i|x_i|$. Write $b(\ell_p^d)$ for the co…

Let $\mathbb M^d$ be a $d$-dimensional Minkowski normed space, and let $b(\mathbb M^d)$ be the least positive integer $k$ such that every bounded non-singleton subset of…

Let $(\mathbb R^n,F)$ be a Minkowski space, and let $\boldsymbol{\Delta}$ denote its Finsler Laplacian. The mean value property refers to the property that $\boldsymbol{\Delta}$-ha…

Cardinality conjecture. A $k$-distance set in $X$ has at most