General Mathematics, Vol. 5, No. 1 - 4, pp. 377-384, 1995

Alessandro Savo -- Estimates of the Heat Content on a Class of Domains

Abstract: We give sharp upper and lower bounds of the heat content of a domain in a Riemannian manifold. These bounds hold for all values of time, under the assumption that the Ricci curvature of the domain and the mean curvature of its boundary are both non-negative. These estimates extend to convex sets of the Euclidean space having arbitrary boundary; in that case, we also give an upper bound of the trace of the heat kernel.

Classification (MSC91): 58G25

Keywords: Distance function, heat content, asymptotic expansions

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