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On the upper estimate of the heat kernel of a complete Riemannian manifold

Siu Yuen Cheng Peter Li Shing-Tung Yau

Differential Geometry mathscidoc:1912.43481

American Journal of Mathematics, 103, (5), 1021-1063, 1981.10
Let M be a complete non-compact Riemannian manifold whose sectional curvature is bounded between two constants-k and K. Then one expects that the heat diffusion in such a manifold behaves like the heat diffusion in Euclidean space. The purpose of this paper is to give a justi-fication of such a statement.
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@inproceedings{siu1981on,
  title={On the upper estimate of the heat kernel of a complete Riemannian manifold},
  author={Siu Yuen Cheng, Peter Li, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203525842265045},
  booktitle={American Journal of Mathematics},
  volume={103},
  number={5},
  pages={1021-1063},
  year={1981},
}
Siu Yuen Cheng, Peter Li, and Shing-Tung Yau. On the upper estimate of the heat kernel of a complete Riemannian manifold. 1981. Vol. 103. In American Journal of Mathematics. pp.1021-1063. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203525842265045.
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