2019/06/20 by Fei He, Changliang Wang, He, Fei +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.1906.08750
32 pages
arxiv created 2019/06/20 · openalex publication_date 2019/06/20 · arxiv updated 2019/06/21 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
In this note, we establish certain regularity estimates for the spinor flow introduced and initially studied in \citeAWW2016. Consequently, we obtain that the norm of the second order covariant derivative of the spinor field becoming unbounded is the only obstruction for long-time existence of the spinor flow. This generalizes the blow up criteria obtained in \citeSc2018 for surfaces to general dimensions. As another application of the estimates, we also obtain a lower bound for the existence time in terms of the initial data. Our estimates are based on an observation that, up to pulling back by a one-parameter family of diffeomorphisms, the metric part of the spinor flow is equivalent to a modified Ricci flow.