The disk property of coverings of 1-convex surfaces
  Let $X$ be an 1-convex surface and $p:\tilde X\to X$ an (unbranched) covering map. We prove that if $\tilde X$ does not contain an infinite Nori string of rational curves then $\tilde X$ satisfies the discrete disk property. 
M. Col\c{t}oiu, C. Joi\c{t}a
math.CV