7 problems

Let $k,m\in\mathbb{N}$ and let $N(k,m)$ be the dimension threshold appearing in the higher-order GJMS geometric Aubin set conjecture for conformal manifolds virtually conformal to…

The higher-order GJMS geometric Aubin set conjecture. The set $\mathscr{A}_{n,2k}$ is a geometric Aubin set for $L_{2k}$.

Green function rigidity conjecture. Then $(M,g)$ is a round sphere.

Let $n\geq 2$, let $\mathbb{S}^n$ be the round sphere, let $P_{\mathbb{S}^n}$ denote its GJMS operator, let $Q_{g_{\mathbb{S}^n}}=(n-1)!/2$ be its constant $Q$-curvature, and let…

Let $P_{2N}^{res}(\lambda)$ be the recursively defined residue-family polynomial of degree $N-1$ built from the GJMS-operators, and let ${\mathcal M}_{2N}$ be the associated operat…

Eighth-order recursive formula.

Let $(M,g)$ be a locally conformally flat Riemannian manifold of dimension $n\geq3$. For $N\geq1$, let ${\mathcal M}_{2N}$ denote the operator defined from the recursive constructi…