5 problems

For given $m \in \mathop{\mathrm{{\Bbb N}}}\nolimits$, $\kappa \in \mathop{\mathrm{{\Bbb R}}}\nolimits$ and $v,D>0$, consider connected oriented closed Riemannian manifolds…

Let $g_{(a,b,c)}$ be the homogeneous metric on the Lie group $\operatorname{SU}(2)$ or $\operatorname{SO}(3)$ determined by positive parameters $a,b,c$. For the Hodge Laplacian…

Lott's conjecture. There exists a positive constant $C(n,\kappa,\nu,D)>0$, depending only on $n$, $\kappa$, $\nu$, and $D$, such that

For given $m \in \mathop{\mathrm{{\Bbb N}}}\nolimits$, $\kappa \in \mathop{\mathrm{{\Bbb R}}}\nolimits$ and $v,D>0$, consider connected oriented closed Riemannian manifolds…

Let $M$ be a compact Kähler manifold, and let $(p,q)$-forms be differential forms of bidegree $(p,q)$. A form is primitive if it is annihilated by the appropriate adjoint Lefschetz…