Exterior Schwarzschild initial data for degenerate apparent horizons

Albert Chau, Adam Martens

In this note we show that if $g$ is a smooth Riemannian metric on ${\mathbb{S}}^2$ such that the first eigenvalue of the operator $L_g:=-{\Delta }_g+K_g$ satisfies ${\lambda }_1(L_g)=0$ then $(\math…