I have some problem when I read Entropy and heat kernel bounds on a Ricci flow background.
In the page 6 (I don't know why I can't upload picture), I don't know what is the mean of the coupled of heat operator coupled with Ricci flow. The heat operator is $$ \square = \partial_t -\Delta_{g_t} $$
Does it only means that the $g_t$ of $\Delta_{g_t}$ satisfy Ricci flow ?