Regularity estimates for the gradient flow of a spinorial energy functional

He, Fei; Wang, Changliang

doi:10.4310/MRL.2021.v28.n4.a7

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Regularity estimates for the gradient flow of a spinorial energy functional

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Wang, Changliang
Max Planck Institute for Mathematics, Max Planck Society;

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https://dx.doi.org/10.4310/MRL.2021.v28.n4.a7
(Publisher version)

https://doi.org/10.48550/arXiv.1906.08750
(Preprint)

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Citation

He, F., & Wang, C. (2021). Regularity estimates for the gradient flow of a spinorial energy functional. Mathematical Research Letters, 28(4), 1125-1173. doi:10.4310/MRL.2021.v28.n4.a7.

Cite as: https://hdl.handle.net/21.11116/0000-0009-B8A6-C

Abstract

In this article, we establish certain regularity estimates for the spinor flow
introduced and initially studied in \cite{AWW2016}. 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 \cite{Sc2018}
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.