2007/07/17 by Ye, Rugang
#53C20 (Primary) #53C21 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.0707.2424
We derive a logarithmic Sobolev inequality along the Ricci flow without any restriction on time, which depends only on the initial metric via rudimentary geometric data, assuming only that a certain first eigenvalue is positive. As a consequence we obtain a uniform Sobolev inequality along the Ricci flow without any restriction on time. One application of it is a uniform kappa-noncollapsing estimate which holds true for all time. We also obtain similar results for bounded time without assuming the eigenvalue condition. The results extend to the Ricci flow with surgeries.