4 problems

Positive mass conjecture for arbitrary asymptotically hyperbolic ends. The mass functional of the end $\mathcal{E}$ is timelike future-directed or zero.

Exponential wave trace remainder conjecture. The remainder $A$ is smooth on $(0,\infty)$, and there exist $C,k>0$, depending only on $n$, $k_1$, and $k_2$, such that

Let $k<\frac n2$ and let $\mathcal{M}^n$ be a complete asymptotically hyperbolic manifold of decay order $\tau>\frac{n}{k+1}$ with finite integral … Assume the dominant energy cond…

The Einstein-scalar field constraint equations arise as the constraints on initial data for the Einstein field equations. In the constant mean curvature (CMC) case, the mean curvat…