4 problems

Let $(M,g)$ be a complete, noncompact manifold with finitely many ends, each end outside a compact set diffeomorphic to a spherical shell. Assume that $M$ has everywhere positive R…

Let $M$ be a properly embedded minimal surface in $\mathbb{R}^3$ with at least two ends, and let its ends be linearly ordered by relative height with respect to its horizontal limi…

Davis-complex conjecture. The spaces $D(\widetilde{X})$ and $D(\widetilde{X}')$ are not simply connected at infinity; consequently, neither is homeomorphic to $\mathbb R^4$. In par…

Let $L$ be a proper leaf of a codimension one $C^2$ foliation on a compact manifold. The end-type invariant $\xi(L)$ is the invariant used to classify the ends of $L$. Cantor finit…