Uniform Sobolev inequalities for manifolds evolving by Ricci flow
| dc.creator | Hsu, Shu-Yu | |
| dc.date | 2007-08-07 | |
| dc.date.accessioned | 2026-07-07T08:22:34Z | |
| dc.date.available | 2026-07-07T08:22:34Z | |
| dc.description | 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 $λ_0(g_0)$ be the first eigenvalue of the operator $-Δ_{g_0} +\frac{R(g_0)}{4}$ 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 $λ_0(g_0)>0$. As a consequence we extend Perelman's local $κ$-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 $λ_0(g_0)>0$. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/0708.0893 | |
| dc.identifier | http://arxiv.org/abs/0708.0893 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135694 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58J35, 53C2x, 46E35 | |
| dc.title | Uniform Sobolev inequalities for manifolds evolving by Ricci flow | |
| dc.type | text |