3 problems

Let $\Phi_0$ be a conformal factor and let $u$ be a sufficiently small perturbation in the relevant Sobolev space. Set $\Phi=\Phi_0+u$. Small-perturbation conjecture. If $u$ is sma…

Let $\u\in H'^2_{-1/2}$ be the deformation variable and let the conformal factor be … Assume that $\Phi_0>0$. Positivity conjecture. If $u$ is sufficiently small, then $\Phi$ is po…

Let $t$, $\gamma_N$, $\mu$, and $\eta$ be the parameters in the reduced conformal constraint system, and suppose the small-TT hypotheses of the Small-TT Results theorem hold, namel…