Some local maximum principles along Ricci flows
Some local maximum principles along Ricci flows
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DOI：
10.4153/s0008414x20000772
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
Man-Chun Lee;Luen-Fai Tam
中科院分区：
文献类型：
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作者：
Man-Chun Lee;Luen-Fai Tam
本文沿着Ricci流g（t）$在满足$\mathrm {Ric}（g（t））\le {\alpha } t^{-1}$（t>0 $）的条件下得到了一个局部极大值原理.作为应用，我们将证明在此条件下，各种曲率对t>0仍然是非负的，只要它们初始是非负的。这些结果推广了紧致流形或具有有界曲率的完备非紧流形上的Ricci流的相应结果。将上述最大值原理与Dirichlet热核估计相结合，我们还对Bamler等人[1]的Hochard [15]局部化形式的最大值原理给出了一个更直接的证明，证明了当t>0$时，Ricci流沿着各种曲率的下界.
Abstract In this work, we obtain a local maximum principle along the Ricci flow $g(t)$ under the condition that $\mathrm {Ric}(g(t))\le {\alpha } t^{-1}$ for $t>0$ for some constant ${\alpha }>0$ . As an application, we will prove that under this condition, various kinds of curvatures will still be nonnegative for $t>0$ , provided they are non-negative initially. These extend the corresponding known results for Ricci flows on compact manifolds or on complete noncompact manifolds with bounded curvature. By combining the above maximum principle with the Dirichlet heat kernel estimates, we also give a more direct proof of Hochard’s [15] localized version of a maximum principle by Bamler et al. [1] on the lower bound of different kinds of curvatures along the Ricci flows for $t>0$ .