In this paper, we prove local existence of a Ricci de Turck flow starting at a space with incomplete edge singularities and flowing for a short time within a class of incomplete edge manifolds. We derive regularity properties for the corresponding family of Riemannian metrics and discuss boundedness of the Ricci curvature along the flow. For Riemannian metrics that are sufficiently close to a flat incomplete edge metric, we prove long-time existence of the Ricci de Turck flow. Under certain conditions, our results yield existence of Ricci flow on spaces with incomplete edge singularities. The proof works by a careful analysis of the Lichnerowicz Laplacian and the Ricci de Turck flow equation.

在本文中，我们证明了Ricci de Turck流的局部存在，该流从具有不完整的边缘奇异点的空间开始，并在一类不完整的边缘流形中短时间内流动。我们导出了相应黎曼度量族的正则性质，并讨论了沿流动的Ricci曲率的有界性。对于足够接近平坦不完整边缘度量的黎曼度量，我们证明了Ricci de Turck流的长期存在。在某些条件下，我们的结果导致在具有不完整边缘奇点的空间上存在Ricci流。该证明通过仔细分析Lichnerowicz Laplacian和Ricci de Turck流动方程而起作用。