5 problems

Bray–Khuri warping-factor conjecture. There exists a warping factor $\phi$ that can be found by coupling the generalized Jang equation to the conformal flow of metrics, and that yi…

Bray–Khuri boundary-condition conjecture. The Neumann-type condition

Spacetime Penrose inequality conjecture. The RPI may be used to prove a version of the Penrose Inequality for slices of spacetimes, using a generalization of the Jang equation.

Let $(M,g,k)$ be asymptotically flat Cauchy data with an outermost generalized apparent horizon boundary $\Sigma$. Define … … where $v=\phi\nabla f/(1+\phi^2|df|_g^2)^{1/2}$. Jang–…

Let $f$ and $\phi$ be associated with the generalized Jang equation, with $\phi$ smooth and strictly positive. Generalized Jang blowup conjecture. The blowup properties of the gene…