Extrema of curvature functional on the space of metrics on 3-manifolds (Q1357760)

This article is an extensive study of some classical variational problems on closed oriented 3-manifolds. The author concentrates on functionals for Riemann and (total) scalar curvature. It is the second part in a planned series of papers regarding the Thurston geometrization conjecture on the geometry of critical metrics. The main results include a convergence theorem for the existence of critical metrics of the Riemann curvature functional. Results of Cheeger-Gromov theory are extended to the square integrable case.