A note on a heat invariant and the Ricci flow on surfaces

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In this short note，we consider the monotonicity of the heat invariant a2 (g) for a Riemannian metric g under the normalized Ricci flow on a closed surface. We show that a2(g(t)) is decreasing under the normalized Ricci flow g(t) in the space of metrics of non-positive curvature.

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