Ricci curvature integrals, local functionals, and the Ricci flow
نویسندگان
چکیده
Consider a Riemannian manifold ( M m , g stretchy="false">) (M^{m}, g) whose volume is the same as standard sphere S Subscript r o u n d S r o u n d encoding="application/x-tex">(S^{m}, g_{round}) . If alttext="p greater-than StartFraction Over 2 EndFraction"> p > 2 encoding="application/x-tex">p\!>\!\frac {m}{2} and alttext="integral Underscript Endscripts left-brace R c minus left-parenthesis 1 right-parenthesis right-brace p v"> ∫ { R c −<!-- − <mml:mn>1 } v encoding="application/x-tex">\int _{M}\! \left \{ Rc\!-\!(m\!-\!1)g\right \}_{-}^{p} dv sufficiently small, we show that normalized Ricci flow initiated from will exist immortally converge to sphere. The choice of alttext="p"> encoding="application/x-tex">p optimal.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2023
ISSN: ['2330-0000']
DOI: https://doi.org/10.1090/btran/155