Consider the solution $g_t$ to the Ricci flow equation $\frac{\partial g}{\partial t} = -2\text{Ric }g$ on a compact manifold $M$ with initial metric $g_0$. This is probably very elementary, but I was wondering how can we prove that the solution $g_t$ is smooth in space? Also, as far as I know, the solution $g_t$ is smooth in time as well. Is there an easy proof for that? Thanks!
2026-03-25 16:01:28.1774454488
Smoothness of Ricci flow
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