4 problems

Shen's conjecture. There are non-trivial positively complete, projectively flat Finsler metrics of constant curvature

Non-Randers constant flag curvature conjecture. Except for Randers metrics, there does not exist any non-locally-projectively-flat regular general $(\alpha,\beta)$-metric with cons…

Local projective flatness conjecture. The metric $F$ must be locally projectively flat.

Let $F=F(x,y)$ be a projective spherically symmetric Finsler metric with constant flag curvature on a convex domain $\Omega\subseteq\mathbb{R}^n$. A Finsler metric is reversible wh…