A universal bound on the gradient of logarithm of the heat kernel for manifolds with bounded Ricci curvature |
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Authors: | A Engoulatov |
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Institution: | Laboratoire de mathématiques, Bâtiment 425, Université Paris-Sud, F-91405 Orsay, France |
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Abstract: | We derive a gradient estimate for the logarithm of the heat kernel on a Riemannian manifold with Ricci curvature bounded from below. The bound is universal in the sense that it depends only on the lower bound of Ricci curvature, dimension and diameter of the manifold. Imposing a more restrictive non-collapsing condition allows one to sharpen this estimate for the values of time parameter close to zero. |
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Keywords: | Ricci curvature Diffusion process Heat kernel Gradient estimate |
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