6 problems

Let $n\geq 3$, let $N\in\mathds{N}$, and let $\varepsilon>0$ be as in the preceding multiplicity result: for…

Let $(X,g_+)$ be a conformally compact Einstein manifold with compactification $(\overline X,\overline g)$ and boundary $N$, and suppose that $\Lambda^\gamma(N,[\overline g|_N])>0$…

Consider solutions $v\colon\mathbb{R}\to\mathbb{R}$ of the fractional equation … that satisfy … Here $P$ is the nonlocal operator … with the kernel $K$ defined by the fractional co…

Fractional positive mass conjecture. The constant term $A$ in this Green's function expansion is nonnegative, and is positive unless the underlying Poincaré–Einstein manifold is th…

Let $\gamma \in (0,1)$, $n > 2\gamma$, and let $(X^{n+1},g^+)$ be Poincaré–Einstein. Suppose that $\Lambda^{\gamma}(M,[\hat{h}])>0$ and that either $(M^n,[\hat{h}])$ is locally con…

Fractional CR Yamabe solvability conjecture. If