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Ancient and expanding spin ALE Ricci flows

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arxiv 2407.18438 v1 pith:H45457VK submitted 2024-07-26 math.DG math-phmath.APmath.MP

Isaac M. Lopez , Tristan Ozuch (Massachusetts Institute of Technology) This is my paper · ORCID
classification math.DGmath-phmath.APmath.MP
keywords spinancientflowsinfinityricciexpandingfunctionalgroups
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abstract

We classify spin ALE ancient Ricci flows and spin ALE expanding solitons with suitable groups at infinity. In particular, the only spin ancient Ricci flows with groups at infinity in $SU(2)$ and mild decay at infinity are hyperk\"ahler ALE metrics. The main idea of the proof, of independent interest, consists in showing that the large-scale behavior of Perelman's $\mu$-functional on any ALE orbifold with non-negative scalar curvature is controlled by a renormalized $\lambda_{\mathrm{ALE}}$-functional related to a notion of weighted mass.

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  1. Uniqueness of asymptotically conical K\"ahler-Ricci flow

    math.DG 2025-04 accept novelty 6.0 of 10

    A complete Kähler-Ricci flow coming out of a Kähler cone must be the self-similar soliton flow when it shares the cohomology class, a Killing field, and curvature bounds.

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