On convergence criteria for the coupled flow of Li–Yuan–Zhang
On convergence criteria for the coupled flow of Li–Yuan–Zhang
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DOI：
10.1007/s00209-019-02272-2
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发表时间：
2018-08
影响因子：
0.8
通讯作者：
Teng Fei;B. Guo;D. Phong
中科院分区：
文献类型：
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作者：
Teng Fei;B. Guo;D. Phong
引入了一种依赖于参数的单参数耦合流族，当它减少到具有(1,1)-形式的度量的耦合流时，最近由Li， Y. Yuan和Y. Zhang提出。它特别表明，对于所有阶导数的估计将遵循和的估计。与适当调整的能量泛函的单调性一起，这可以应用于建立流在某些情况下的收敛性，包括在黎曼曲面上。对于存在耦合的流的单调性和收敛性，目前所知甚少，而这样的条件似乎是新的，将来可能会有用。
A one-parameter family of coupled flows depending on a parameteris introduced which reduces whento the coupled flow of a metricwith a (1, 1)-formdue recently to Y. Li, Y. Yuan, and Y. Zhang. It is shown in particular that, for, estimates for derivatives of all orders would follow fromestimates forand. Together with the monotonicity of suitably adapted energy functionals, this can be applied to establish the convergence of the flow in some situations, including on Riemann surfaces. Very little is known as yet about the monotonicity and convergence of flows in presence of couplings, and conditions such asseem new and may be useful in the future.