Gap Theorem on locally conformally flat manifold

2025/04/11 by Hsiao, Ming, Lee, Man-Chun
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.08189

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.

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• Gap Theorem on Riemannian manifolds using Ricci flow
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