The logarithmic Sobolev inequality along the Ricci flow

Details The logarithmic Sobolev inequality along the Ricci flow The logarithmic Sobolev inequality along the Ricci flow

2007-07-17

arxiv.org/abs/0707.2424v4

Mathematics

Differential Geometry

One appendix is added. A theorem on the Sobolev inequality along the Ricci flow with surgeries of Perelman is added. Two nonlo

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The logarithmic Sobolev inequality along the Ricci flow does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The logarithmic Sobolev inequality along the Ricci flow, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The logarithmic Sobolev inequality along the Ricci flow will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-562267