Rational connectedness and order of non-degenerate meromorphic maps   from\ ${\bf C}^n$
  We show that an $n$-dimensional compact K\"ahler manifold $X$ admitting a non-degenerate meromorphic map $f:{\bf C}^n\to X$ of order $\rho_f<2$ is rationally connected. 
Fr\'ed\'eric Campana, J\"org Winkelmann
math.AG math.CV