论文标题
与时间相关的歧管上的热流
Heat flow on time-dependent manifolds
论文作者
论文摘要
在最小的假设下，我们为在研究通过奇异性的RICCI流动量身定制的最小假设下，为时间依赖性的Riemannian歧管建立了有效的存在和独特性。要点是，我们的估计仅取决于体积度量的对数导数的上限。特别是，我们的估计值适用于下面有标量曲率的任何RICCI流动，而这样的下限当然仅取决于初始数据。
We establish effective existence and uniqueness for the heat flow on time-dependent Riemannian manifolds, under minimal assumptions tailored towards the study of Ricci flow through singularities. The main point is that our estimates only depend on an upper bound for the logarithmic derivative of the volume measure. In particular, our estimates hold for any Ricci flow with scalar curvature bounded below, and such a lower bound of course depends only on the initial data.
