# Heat Kernel Comparison on Alexandrov Spaces with Curvature Bounded Below

@article{Renesse2004HeatKC, title={Heat Kernel Comparison on Alexandrov Spaces with Curvature Bounded Below}, author={Max-K. von Renesse}, journal={Potential Analysis}, year={2004}, volume={21}, pages={151-176} }

In this paper the comparison result for the heat kernel on Riemannian manifolds with lower Ricci curvature bound by Cheeger and Yau (1981) is extended to locally compact path metric spaces (X,d) with lower curvature bound in the sense of Alexandrov and with sufficiently fast asymptotic decay of the volume of small geodesic balls. As corollaries we recover Varadhan's short time asymptotic formula for the heat kernel (1967) and Cheng's eigenvalue comparison theorem (1975). Finally, we derive an…

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