3 problems

Yau's conjecture. For $n\geq 3$, any closed $2n$-manifold admitting an almost complex structure will also admit a complex structure.

Let $(M,J_0)$ be a Fano manifold admitting a Kähler-Ricci soliton $\omega_{KS}\in 2\pi c_1(M,J_0)$. Let $H_1$ be the operator whose negative eigenspaces define the linear subspace…

Let $M$ be a smooth manifold equipped with a Riemannian metric $g$. Consider the space of complex structures on $M$ that are orthogonal to $g$, together with its dimension and numb…