The (logarithmic) Sobolev inequalities along geometric flow and applications
The (logarithmic) Sobolev inequalities along geometric flow and applications
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DOI：
10.1016/j.jmaa.2015.09.034
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发表时间：
2015-02
期刊：
影响因子：
--
通讯作者：
Shouwen Fang;Taotao Zheng
中科院分区：
文献类型：
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作者：
Shouwen Fang;Taotao Zheng
对于一类几何流，我们直接得到了（对数）Sobolev不等式及其在不同因子下的等价性，并得到了长时不坍缩和不膨胀的性质，推广了Ricci流、李氏-Ricci流或谐波-Ricci流的结果。作为应用，对于具有非负截面曲率的洛伦兹空间中的平均曲率流和Fano流形上的扭曲Kähler-Ricci流，我们得到了上述结果。
For some class of geometric flows, we obtain the (logarithmic) Sobolev inequalities and their equivalence up to different factors directly and also obtain the long time non-collapsing and non-inflated properties, which generalize the results in the case of Ricci flow or List–Ricci flow or harmonic-Ricci flow. As applications, for mean curvature flow in Lorentzian space with nonnegative sectional curvature and twisted Kähler–Ricci flow on Fano manifolds, we get the results above.