Rigidity theorems on smooth metric measure spaces with weighted Poincaré inequality

We obtain some results on the rigidity of complete smooth metric measure spaces with weighted Poincaré inequality, which generalize previous results in Cheng and Zhou (2009), Dung (2012), Dung and Sung (2013), Fu and Li (2010), Fu and Yang (2012), Lam (2010), Li (2005), Li and Wang (2001, 2006), Wang (2012). As an application, we prove that a complete (n−1)2n2-stable minimal hypersurface in Rn+1Rn+1 with n≥3n≥3 must have only one end.