A generalization of Hamilton's gradient estimate (Q413680)

The author generalizes Hamilton's gradient estimate for the ``carré du champ'' of a bounded positive solution of the heat equation on a Riemannian manifold with lower bounded Ricci curvature. The generalization takes the form of a \(\Phi\)-gradient estimate under a curvature-dimension inequality. Hamilton's estimate is recovered by taking \(\Phi (x) = x \log x\).