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The Quarterly Journal of Mathematics 2001 52(2):171-180; doi:10.1093/qjmath/52.2.171
© 2001 by Oxford University Press
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Heat Kernel Estimates with Application to Compactness of Manifolds

Fu-Zhou Gong1 and Feng-Yu Wang2

1 Institute of Applied Mathematics, Science Academy of China, Beijing, China. 2 Department of Mathematics, Beijing Normal University, Beijing 100875, China.

Li and Yau type two-sided heat kernel bounds are obtained for symmetric diffusions under a curvature–dimension condition, where the heat kernel upper bound is established for a more general case. As an application, the compactness of manifolds is studied using heat kernels. In particular, a conjecture by Bueler is proved.


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