Convergence Stability for Ricci Flow
Convergence Stability for Ricci Flow
复制标题
DOI：
10.1007/s12220-018-00132-9
复制
发表时间：
2018-05
期刊：
影响因子：
--
通讯作者：
Eric Bahuaud;Christine Guenther;J. Isenberg
中科院分区：
文献类型：
--
作者：
Eric Bahuaud;Christine Guenther;J. Isenberg
几何流动的收敛稳定性原理是流动对初始条件的连续依赖性和不动点稳定性的结合。这意味着如果从初始状态流出的流始终存在并且收敛到一个稳定的不动点，那么从附近开始的解的流也收敛到固定点。我们在Ricci流的情况下展示了这一点，仔细地证明了对初始条件的连续依赖性。为了简化几何流动方程，通常对初始几何形状进行对称性假设。作为我们结果的一个应用，我们将已知的收敛结果推广到这些初始数据的开集，其中包含没有对称性的几何。
The principle ofconvergence stabilityfor geometric flows is the combination of the continuous dependence of the flow on initial conditions, with the stability of fixed points. It implies that if the flow from an initial stateexists for all time and converges to a stable fixed point, then the flows of solutions that start nearalso converge to fixed points. We show this in the case of the Ricci flow, carefully proving the continuous dependence on initial conditions. Symmetry assumptions on initial geometries are often made to simplify geometric flow equations. As an application of our results, we extend known convergence results to open sets of these initial data, which contain geometries with no symmetries.