论文标题
有界的RICCI曲率和正标度曲率在单数Ricci de Turck流动下
Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow
论文作者
论文摘要
在本文中，我们考虑了带有孤立圆锥形奇点的空间的Ricci de turck流动，该空间可保留沿流动的锥形结构。我们确定给定的RICCI曲率的初始规律性沿流程保留。此外，在其他假设下，标量曲率的阳性被保留在这种流程下，反映了Ricci流的标准特性在紧凑的歧管上。分析难度是沿流动圆锥形尖端处标量曲率的先验低规律性，因此最大原理不适用。我们将这项工作视为研究沿单数RICCI流动曲率操作员阳性的第一步。
In this paper we consider a Ricci de Turck flow of spaces with isolated conical singularities, which preserves the conical structure along the flow. We establish that a given initial regularity of Ricci curvature is preserved along the flow. Moreover under additional assumptions, positivity of scalar curvature is preserved under such a flow, mirroring the standard property of Ricci flow on compact manifolds. The analytic difficulty is the a priori low regularity of scalar curvature at the conical tip along the flow, so that the maximum principle does not apply. We view this work as a first step toward studying positivity of the curvature operator along the singular Ricci flow.
