Wave equations associated to Liouville systems and constant mean   curvature equations
  We study the wave analog of the Liouville equation and the constant mean curvature equations in 2 space dimensions, which are energy critical. We exhibit a blow-up criteria for the former using tools from conformal geometry, and we exhibit finite time blow-up for the latter under suitable assumptions on the initial data. 
Sagun Chanillo, Po-Lam Yung
math.AP math.CA math.DG