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In this paper, we establish a Bochner type formula on Alexandrov spaces with Ricci curvature
bounded below. Yau’s gradient estimates for harmonic functions is also obtained on Alexandrov
spaces.
On gradient estimates for a nonlinear parabolic equation on Riemannian manifolds
Nonlinear parabolic equations Gradient estimates
2010/9/25
Let (M,g) be a complete noncompact Riemannian manifold. In this note, we derive a local gradient estimate for positive solution to a simple nonlinear parabolic equation