3 problems

Consider the setting of Theorem … , the spacetime is future causally geodesically complete. The surrounding discussion says that the answer is expected to be affirmative for…

Critical-index conjecture. All solutions exist for all time if $k\geq \frac{n}{2}+1$, whereas for $k<\frac{n}{2}+1$ there are always some solutions that break down in finite time.…

Let $G^1$ and $G^2$ be smooth, weak Riemannian metrics on an infinte-dimensional Banach manifold $\mathcal H$. Assume that $G^2$ is uniformly stronger than $G^1$, both metrics admi…