# 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}
}
• Published 2007
• Mathematics
• Archiv der Mathematik
• 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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