16 problems

Let $F$ be a Minkowski norm on $\mathbb{R}^n$ with Hessian metric $g$, where $n\geq 3$. Laugwitz's conjecture. If $g$ is flat on $\mathbb{R}^n\backslash\{0\}$, then $F$ is Euclidea…

Füredi–Lagarias–Morgan conjecture. There exists an $\epsilon>0$ such that every equilateral set in $M$ satisfies

Let $\mathbb{M}_Z^n$ be the $n$-dimensional Minkowski space whose unit ball is $\operatorname{conv}([0,1]^n\cup[-1,0]^n)$. An equilateral set is a set of points whose pairwise dist…

Let $\mathbb{M}^n$ be a piece-wise differentiable, elliptic Minkowski space, and let $s(\mathbb{M}^n)$ denote the maximum degree of a Steiner point in a Steiner minimal tree in…

Let $\mathbb{M}^n$ be an $n$-dimensional Minkowski space, and let $s(\mathbb{M}^n)$ denote the maximum degree of a Steiner point in a Steiner minimal tree in $\mathbb{M}^n$. Morgan…

Cieslik's conjecture. The maximum degree satisfies

For real $c>1$, consider the Minkowski spheres … The kissing number is the maximum number of non-overlapping congruent spheres tangent to a given sphere. Conjecture on Minkowski-sp…

Let $p$ be the parameter of the family of Minkowski balls and let the covering constant be the associated covering invariant. Conjecture on the curve of maxima. The curve of maxima…

Alonso–Martini–Wu conjecture. In any non-Euclidean Minkowski plane $X$, there exist $x,y\in S_X$, with $x\neq\pm y$, such that

Let $p$ range over $1<p<\infty$, and consider the curve whose value at $p$ is the maximum covering constant for the Minkowski ball $D_p$. The curve of maxima conjecture. The curve…

Let the constructed lens be the region containing the fast passengers, with its boundary formed by the curves described above. Minimal-area conjecture. Without proof, we conjecture…

Let $u$ be a solution of … where $C>1$ and the graph of $u$ is an entire strictly spacelike hypersurface in Minkowski space. Aarons's conjecture. The solution $u$ is either rotatio…

For each arc $\alpha\in\mathscr{A}$, let $\underline{\alpha}$ be a minimally intersecting geodesic representative and let $p_{\alpha}$ be a waist; with widths $m_{\alpha}$, define…

Let a smooth Minkowski space be a finite-dimensional real normed space whose norm is smooth away from the origin, and let an adjoint-abelian operator be a linear operator $A$ satis…

Let $N$ be a set of $n$ terminals in a Minkowski plane $M$ with unit ball $B$, and let $T_S$ and $T_{\mathrm{opt}}$ be a $d_M$-SMT and a $d_M$-MSPT on $N$, respectively. Minkowski-…

Equilateral-triangle side-length conjecture. One has