Ricci curvature integrals, local functionals, and the Ricci flow

Autor:	Ma, Yuanqing, Wang, Bing
Rok vydání:	2021
Předmět:	Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	Consider a Riemannian manifold $(M^{m}, g)$ whose volume is the same as the standard sphere $(S^{m}, g_{round})$. If $p>\frac{m}{2}$ and $\int_{M} \left\{ Rc-(m-1)g\right\}_{-}^{p} dv$ is sufficiently small, we show that the normalized Ricci flow initiated from $(M^{m}, g)$ will exist immortally and converge to the standard sphere. The choice of $p$ is optimal.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.02449 Zobrazit plný text záznamu View this record from Arxiv