The Bounded L2 Curvature Conjecture

Understand

This is the main paper in a sequence in which we give a complete proof of the bounded $L^2$ curvature conjecture.

• More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the $L^2$-norm of the curvature and a lower bound on the volume radius of the corresponding initial data set.
• We note that though the result is not optimal with respect to the standard scaling of the Einstein equations, it is nevertheless critical with respect to its causal geometry.
• Indeed, $L^2$ bounds on the curvature is the minimum requirement necessary to obtain lower bounds on the radius of injectivity of causal boundaries.