Abstract

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) ≥−ε ∕ (1 + d(x)^2+δ), with δ > 0 and ε > 0 suficiently small.

Keywords

harmonic functions, log gradient bound, stablility

Mathematical Subject Classification

Primary: 58J05, 58J35

Authors