As on arXiv
Abstract
In this work, we study a gap phenomenon in locally conformally flat Riemannian manifolds with non-negative Ricci curvature. We construct complete solutions to the Yamabe flow that exhibit instantaneous bounded curvature as they evolve. Using this, we demonstrate that if the curvature decays quickly enough in an integral sense, then the manifold must be flat. This partially generalizes the results of Chen-Zhu and Ma.
Comments: 19 pages. All comments are welcome
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Topics Yamabe flow · Shared terms “locally conformally”, “conformally flat”, “flat manifolds”
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Topics Yamabe flow · Shared terms “locally conformally”, “conformally flat”, “flat manifolds”
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Topics Yamabe flow · Shared terms “phenomenon”
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Same author Man-Chun Lee · Shared terms “gap theorem”, “curvature decay”, “gap phenomenon”
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Topics Yamabe flow
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Topics Yamabe flow · Shared terms “conformally flat”
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Topics Yamabe flow
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 6C.4The Yamabe Problem and Critical Exponents
Conformal changes of scalar curvature, the Yamabe functional, Aubin's threshold and Schoen's solution, concentration compactness and bubbles, and why Perelman's log-Sobolev minimisers always exist.