Abstract
In this paper, a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established. Applying it to the heat kernel estimate of the operator 1/2 Δ +b, we obtain the Aronson's estimate for the operator 1/2 Δ +b, which can be regarded as an extension of Peter Li and S.T. Yau's heat kernel estimate for the Laplace-Beltrami operator.
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This project is partially supported by the National Natural Science Foundation of China.
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Qian, Z. Diffusion processes on complete riemannian manifolds. Acta Mathematicae Applicatae Sinica 10, 252–261 (1994). https://doi.org/10.1007/BF02006856
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DOI: https://doi.org/10.1007/BF02006856