2 problems

Let $coperatorname{\mathbb{R}P}^2$ be a real projective plane endowed with a Riemannian metric $g$. A closed geodesic is non-contractible if its underlying loop represents a nontri…

Let $\omega_N\subset\mathbb{S}^2$ be a collection of $N$ antipodal points, meaning that $p\in\omega_N$ implies $-p\in\omega_N$. Let $\mathscr{E}_{\log}(\omega_N)$ denote its logari…