Ricci curvature integrals, local functionals, and the Ricci flow
Ricci curvature integrals, local functionals, and the Ricci flow
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DOI：
10.1090/btran/155
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发表时间：
2021-09
期刊：
影响因子：
--
通讯作者：
Yuanqing Ma;Bing Wang
中科院分区：
文献类型：
--
作者：
Yuanqing Ma;Bing Wang
Consider a Riemannian manifold ( M m , g ) (M^{m}, g) whose volume is the same as the standard sphere ( S m , g r o u n d ) (S^{m}, g_{round}) . If p > m 2 p\!>\!\frac {m}{2} and ∫ M { R c − ( m − 1 ) g } − p d v \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 ) (M^{m}, g) will exist immortally and converge to the standard sphere. The choice of p p is optimal.
Consider a Riemannian manifold ( M m , g ) (M^{m}, g) whose volume is the same as the standard sphere ( S m , g r o u n d ) (S^{m}, g_{round}) . If p > m 2 p\!>\!\frac {m}{2} and ∫ M { R c − ( m − 1 ) g } − p d v \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 ) (M^{m}, g) will exist immortally and converge to the standard sphere. The choice of p p is optimal.