Time-analyticity of solutions to the Ricci flow

Original · EN

In this paper, we prove that if g(t) is a smooth, complete solution to the Ricci flow of uniformly bounded curvature on M×[0, Ω], then the correspondence t g(t) is real-analytic at each t₀∈ (0, Ω). The analyticity is a consequence of classical Bernstein-type estimates on the temporal and spatial derivatives of the curvature tensor, which we further use to show that, under the above global hypotheses, for any x₀∈ M and t₀∈ (0, Ω), there exist local coordinates x = xⁱ on a neighborhood U⊂ M of x₀ in which the representation gij(x, t) of the metric is real-analytic in both x and t on some cylinder U× (t₀ -ε, t₀ + ε).