2 problems

Spherical quasi-convexity characterization conjecture. This condition is necessary and sufficient to characterize spherically quasi-convex quadratic functions.

Let $\mathcal{K}(\mathbb{S}^n)$ denote the set of spherically convex bodies, and let $\Omega_s(K)$ be the floating area of $K\in\mathcal{K}(\mathbb{S}^n)$: … For each $K$, let…