Resumen de Stability of the Cheng¿Yau gradient estimate

Qi S. Zhang

• We prove that the Cheng¿Yau gradient estimate on positive harmonic functions on manifolds with nonnegative Ricci curvature is globally stable under certain perturbations of the metric. In some cases, one only needs the condition Ricci(x) =-e / (1 + d(x)2+d), with d > 0 and e > 0 suficiently small.