On the steady state of the heat conduction on a Riemannian symmetric space (Q5966485)

We treat the heat conduction on a Riemannian symmetric space X. Assume that X is embedded into the Oshima compactification \(\tilde X,\) the initial value f is bounded continuous on X and has a limit \(f_{\infty}\) along the Martin boundary. Then we show that the steady state of the heat conduction is a harmonic function which is given by the Poisson integral of \(f_{\infty}\). The behavior of f near the other boundaries has no effect on the steady state. A class of initial functions may be widened to a larger class of functions.