Uniform Sobolev inequalities for manifolds evolving by Ricci flow

Details Uniform Sobolev inequalities for manifolds evolving by Ricci flow Uniform Sobolev inequalities for manifolds evolving by Ricci flow

2007-08-07

arxiv.org/abs/0708.0893v1

Mathematics

Differential Geometry

8 pages

Scientific paper

Let M be a compact n-dimensional manifold, $n\ge 2$, with metric g(t) evolving by the Ricci flow $\partial g_{ij}/\partial t=-2R_{ij}$ in (0,T) for some $T\in\Bbb{R}^+\cup\{\infty\}$ with $g(0)=g_0$. Let $\lambda_0(g_0)$ be the first eigenvalue of the operator $-\Delta_{g_0} +\frac{R(g_0)}{4}$ with respect to g_0. We extend a recent result of R. Ye and prove uniform logarithmic Sobolev inequality and uniform Sobolev inequalities along the Ricci flow for any $n\ge 2$ when either $T<\infty$ or $\lambda_0(g_0)>0$. As a consequence we extend Perelman's local $\kappa$-noncollapsing result along the Ricci flow for any $n\ge 2$ in terms of upper bound for the scalar curvature when either $T<\infty$ or $\lambda_0(g_0)>0$.

Affiliated with

Also associated with

No associations

Rating

Uniform Sobolev inequalities for manifolds evolving by 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 Uniform Sobolev inequalities for manifolds evolving by Ricci flow, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniform Sobolev inequalities for manifolds evolving by Ricci flow will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-170200