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April 2021 A gap theorem for half-conformally flat manifolds
Brian Weber, Martin Citoler-Saumell
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Illinois J. Math. 65(1): 71-96 (April 2021). DOI: 10.1215/00192082-8886951

Abstract

We show that a compact half-conformally flat manifold of negative type with bounded L2 energy, sufficiently small scalar curvature, and a noncollapsing assumption has all Betti numbers bounded in terms of the L2 curvature norm. We give examples of multi-ended bubbles that disrupt attempts to improve these Betti number bounds. We show that bounded self-dual solutions of dω=0 on asymptotically locally Euclidian (ALE) manifold ends display a rate-of-decay gap: they are either asymptotically Kähler, or they have a decay rate of O(r4) or better.

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Brian Weber. Martin Citoler-Saumell. "A gap theorem for half-conformally flat manifolds." Illinois J. Math. 65 (1) 71 - 96, April 2021. https://doi.org/10.1215/00192082-8886951

Information

Received: 1 November 2019; Revised: 5 October 2020; Published: April 2021
First available in Project Euclid: 14 January 2021

Digital Object Identifier: 10.1215/00192082-8886951

Subjects:
Primary: 53C23
Secondary: 53A31 , 53C21

Rights: Copyright © 2021 by the University of Illinois at Urbana–Champaign

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Vol.65 • No. 1 • April 2021
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