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Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].

3 votes

The heat kernel as an exponential of an integral

Actually, I think your second formula might indeed relate the distance on a Riemannian manifold to the heat kernel - see this paper by Varadhan, in which it is shown that if $p(t,x,y)$ is a solution t …
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