3 problems

Let $(M^3,g)$ be an asymptotically Euclidean manifold of order $\tau\in(-1,-\frac{1}{2})$ with respect to a structure of infinity $\Phi_z$ and coordinates $\{z^i\}_{i=1}^3$. Assume…

Let $(M^3,g)$ be an asymptotically Euclidean manifold of order $\tau\in(-1,-\frac{1}{2})$ with respect to a structure of infinity $\Phi_z$ and coordinates $\{z^i\}_{i=1}^3$. Assume…

John ellipsoid half-volume conjecture. The ellipsoid obtained by scaling $B_K$ by a factor of $O(\sqrt{n})$ about its center contains at least half of the volume of $K$.