Asymptotic behavior of conformal metrics with null Q-curvature

2023/08/24 by Mingxiang Li, Li, Mingxiang
Mathematics · Medicine · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Pelvic and Acetabular Injuries

paper · pdf · doi:10.48550/arxiv.2308.12656

Abstract

We describe the asymptotic behavior of conformal metrics related to the GJMS operator in the null case, as the prescribed Q-curvature f₀(x) + λ gradually changes. We show that if one of the maximum points of f₀ is flat up to order n-1, the normalized conformal metrics in the lowest energy level will form exactly one spherical bubble as λ approaches zero using higher order Bol's inequality. This generalizes the result of Struwe (JEMS, 2020) in the two-dimensional case to higher dimensions and helps rule out the slow bubble case discussed by Ngô and Zhang (arXiv:1903.12054) to some degree.

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