4 problems

Ren–Wang's concavity conjecture. Their concavity inequality should hold for all $k$ satisfying

For a hypersurface with prescribed $k$-th elementary symmetric curvature, let $k$ denote the order of the higher-order mean curvature, with $k=1$ corresponding to mean curvature an…

Existence and uniqueness conjecture. There exists a unique $k$-admissible solution $u$ satisfying

Existence conjecture. The equation has a positive solution for an antipodally symmetric curvature function $R(\xi)$.