The strong elliptic maximum principle for vector bundles and   applications to minimal maps
  Based on works by Hopf, Weinberger, Hamilton and Evans, we state and prove the strong elliptic maximum principle for smooth sections in vector bundles over Riemannian manifolds and give some applications in Differential Geometry. Moreover, we use this maximum principle to obtain various rigidity theorems and Bernstein type theorems in higher codimension for minimal maps between Riemannian manifolds. 
Andreas Savas-Halilaj and Knut Smoczyk
math.DG