Holographic Uniformization
  We derive and study supergravity BPS flow equations for M5 or D3 branes wrapping a Riemann surface. They take the form of novel geometric flows intrinsically defined on the surface. Their dual field-theoretic interpretation suggests the existence of solutions interpolating between an arbitrary metric in the UV and the constant-curvature metric in the IR. We confirm this conjecture with a rigorous global existence proof. 
Michael T. Anderson, Christopher Beem, Nikolay Bobev, Leonardo   Rastelli
hep-th math.AP math.DG