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arxiv 2206.09198 v1 pith:WYF537VE submitted 2022-06-18 math.DG math-phmath.APmath.MP

The spinorial energy for asymptotically Euclidean Ricci flow

classification math.DG math-phmath.APmath.MP
keywords flowmanifoldsasymptoticallyenergyeuclideanfunctionalriccispinorial
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This paper introduces a functional generalizing Perelman's weighted Hilbert-Einstein action and the Dirichlet energy for spinors. It is well-defined on a wide class of non-compact manifolds; on asymptotically Euclidean manifolds, the functional is shown to admit a unique critical point, which is necessarily of min-max type, and Ricci flow is its gradient flow. The proof is based on variational formulas for weighted spinorial functionals, valid on all spin manifolds with boundary.

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