论文标题
Lipschitz地图使用谐波图热流的刚度
Rigidity of Lipschitz map using harmonic map heat flow
论文作者
论文摘要
在标量曲率几何形状中的Lipschitz刚度问题的启发下，我们证明，如果闭合的平滑旋转歧管承认距离降低了一个非零程度的连续映射到一个球体，则标量曲率严格少于球体的某个地方，或者地图是距离等距离。此外，该属性还具有具有标态曲率下限的连续指标。这扩展了Cecchini-Hanke-Schick最近工作的结果，并回答了Gromov的问题。该方法基于研究谐波图热流以及从粗糙初始数据的RICCI流程，以减少案例到平滑指标和平滑地图，以便可以应用Llarull的结果。
Motivated by the Lipschitz rigidity problem in scalar curvature geometry, we prove that if a closed smooth spin manifold admits a distance decreasing continuous map of non-zero degree to a sphere, then either the scalar curvature is strictly less than the sphere somewhere or the map is a distance isometry. Moreover, the property also holds for continuous metrics with scalar curvature lower bound in some weak sense. This extends a result in the recent work of Cecchini-Hanke-Schick and answers a question of Gromov. The method is based on studying the harmonic map heat flow coupled with the Ricci flow from rough initial data to reduce the case to smooth metrics and smooth maps so that results by Llarull can be applied.
