7 problems

Let $M$ be complete, let $O$ be a fixed origin, and suppose that for some $r_0>0$ the Ricci curvature is bounded below by $(n-1)/(4r^2)$ whenever $r\geq r_0$. Higher-dimensional Ri…

Compactness conjecture. Is $Min(Q)$ compact?

Compactness characterization conjecture. The following statements are equivalent: $(X,d)$ is compact; and there is a labeled ray $R(l)$ generating $(X_0,d_0)$ such that

Compactness conjecture for minimizing sequences. There is a sequence of Möbius transformations $G_j$ of $\mathbb{R}^3$ such that the surfaces $G_j\circ\mathbf{x}_j(K)$ can be parti…

Equiconsistency conjecture. The existence of $\textbackslash \kappa$ which is $\textbackslash \kappa$-compact is equiconsistent with the existence of a cardinal…

Let $M$ be the underlying manifold, and let $(\varepsilon_i,\Psi_i,{\bm\xi}_i,A_i)$ be a sequence of solutions of the blown-up ADHM$_{1,k}$ Seiberg--Witten equation satisfying … wi…

Let $\Lambda\in\mathcal M_f([0,1])$, and let $\mathcal V^\Lambda_t$ be the tree-valued $\Lambda$-resampling dynamics at time $t$. Write $\mathbb U_c$ for the space of compact metri…