# Journal of Operator Theory

Volume 41, Issue 1, Winter 1999 pp. 93-120.

A Riemannian off-diagonal heat kernel bound for uniformly elliptic operators**Authors**: Mark P. Owen

**Author institution:**Department of Mathematics, King's College London, Strand, London WC2R 2LS, England

**Summary:**We find a Gaussian off-diagonal heat kernel estimate for uniformly elliptic operators with measurable coefficients acting on regions $\Omega \subseteq\real^N$, where the order $2m$ of the operator satisfies $N<2m$. The estimate is expressed using certain Riemannian-type metrics, and a geometrical result is established allowing conversion of the estimate into terms of the usual Riemannian metric on $\Omega$. Work of Barbatis~([1]) is applied to find the best constant in this expression.

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