Abstract：

By introducing a concept generalising several convexity notions we obtain a new Omori-Yaumaximum principle for harmonic maps defined on a stochastically complete manifold. Some of theapplications of this new maximum principle include conformal harmonic maps. an adaptation of aconiecture of Calabi, harmonic immersions with certain energy bounds, wedge theorems forminimal submanifolds of lRn.