Short-time existence for some higher-order geometric flows

Details Short-time existence for some higher-order geometric flows Short-time existence for some higher-order geometric flows

2010-10-20

arxiv.org/abs/1010.4287v1

Mathematics

Differential Geometry

17 pages

Scientific paper

We establish short-time existence and regularity for higher-order flows generated by a class of polynomial natural tensors that, after an adjustment by the Lie derivative of the metric with respect to a suitable vector field, have strongly parabolic linearizations. We apply this theorem to flows by powers of the Laplacian of the Ricci tensor, and to flows generated by the ambient obstruction tensor. As a special case, we prove short-time existence for a type of Bach flow.

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