Geometric properties coded in the long-time asymptotics for the heat equation on 𝑍ⁿ

Bednarchak, Debe

doi:10.1090/S0002-9939-02-06760-6

Geometric properties coded in the long-time asymptotics for the heat equation on $Z^n$
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Proc. Amer. Math. Soc. 131 (2003), 2261-2269 Request permission

Abstract:

This paper investigates connections between the long-time asymptotics of heat distribution on a body $\Omega$ in $Z^n$, and various geometric properties of $\Omega$, starting from an initially constant heat distribution supported on $\Omega$. We use combinatorial and differential geometric methods. We begin the paper with a result in $R^n$.

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