4 problems

Let $M$ be a manifold with an $F$-structure, and suppose the $F$-structure has positive rank. A local splitting structure is a geometric structure associated with the nonpositively…

Let $M^n$ be a manifold, and let $\text{MinVol}(M)$ denote the infimum of the volumes of complete metrics on $M$ with $|\text{sec}_M|\le 1$. Gromov's gap conjecture. There exists a…

In a toroidal degeneration $\pi:\mathcal{X}\rightarrow\Delta$, let $\mathcal{F}$ be the Hamiltonian $F$-structure conjectured on $X_t\cap\mathfrak{U}$ near the multiple intersectio…

Let $n\in \mathbb{N}$. For a closed Kähler $n$-manifold $(M,\omega,J,g)$ with $[\omega]\in H^{2}(M,\mathbb{Z})$, define … An F-structure is understood in the sense of Cheeger–Gromo…