# Uniform approximation of the heat kernel on a manifold

@article{Shamarova2007UniformAO, title={Uniform approximation of the heat kernel on a manifold}, author={E. Shamarova and A. B. Simas}, journal={Archiv der Mathematik}, year={2007}, volume={108}, pages={485-494} }

We approximate the heat kernel h(x, y, t) on a compact connected Riemannian manifold M without boundary uniformly in $$(x,y,t)\in M\times M\times [a,b]$$(x,y,t)∈M×M×[a,b], $$a>0$$a>0, by n-fold integrals over $$M^n$$Mn of the densities of Brownian bridges. Moreover, we provide an estimate for the uniform convergence rate. As an immediate corollary, we get a uniform approximation of solutions of the Cauchy problem for the heat equation on M.

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