3 problems

Torus-bundle conjecture. There exists $\varepsilon=\varepsilon(m,l,\iota)>0$ such that these assumptions imply that $M$ is a torus bundle over $X$. This is presented as an open pro…

Collapsed pseudo-locality conjecture. The asserted curvature estimate should hold even when the initial unit ball is Gromov--Hausdorff close to a lower-dimensional Euclidean ball.…

Suppose a sequence $\{(M_i,g_i)\}\subset \widetilde{\mathcal{M}}_{\rm Rc}(m,\rho,v)$ collapses to a lower-dimensional compact metric space $X$, with … where $k$ is the dimension in…