Base point estimates of the curvature tensor of the Ricci flow

我研究了Ricci流，以得到曲率张量的估计，它只依赖于所讨论的基点处的张量和初始数据。分析与Ricci流的奇异性直接相关，我澄清，作为第一步，目标几乎相同，排除在Ricci-Flat流形上模拟的奇异性，取决于初始数据。我逐渐意识到，排除比表面上看起来要困难得多，需要从全新的角度来看待分析估计的框架。因此，我主要关注对Ricci流本身方程的新解释。具体地说，我将度规的相空间设置为适当的复化，并给出了无限维Kaehler结构，并试图将Ricci流解释为相空间上的动力学系统。到目前为止，我给出了相空间的Kaehler势和全纯矢量场的Cauchy Riemann方程。下一个目标是将Ricci流理解为由合适的矢量场产生的流。

I investigate the Ricci flow to obtain the estimate of the curvature tensor which depends only on the tensor at the base point in question and the initial data. The analysis is directly related to singularity of the Ricci flow and I clarified that the goal is almost identical to exclude the singularity modeled on the Ricci-flat manifold, depending on the initial data, as a first step. I gradually realized that the exclusion is more difficult than it appears, and requires the completely new point of view of the framework of the analytic estimate. Hence I mainly concerned with the new interpretation of the equation of the Ricci flow itself. Specifically, I setup the phase space of the metric as a suitable complexification and gave it a Kaehler structure of infinite dimension and tried to interpret the Ricci flow as a dynamical system on the phase space. So far I specified the Kaehler potential of the phase space and the Cauchy Riemann equation of the holomorphic vector field. The next goal is to understand the Ricci flow as a flow generated by suitable vector field.