On perturbations of the fractional Yamabe problem

2015/01/04 by Woocheol Choi, Choi, Woocheol, Seunghyeok Kim +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1501.00641

openalex publication_date 2015/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The fractional Yamabe problem, proposed by González-Qing (2013, Anal. PDE) is a geometric question which concerns the existence of metrics with constant fractional scalar curvature. It extends the phenomena which were discovered in the classical Yamabe problem and the boundary Yamabe problem to the realm of nonlocal conformally invariant operators. We investigate a non-compactness property of the fractional Yamabe problem by constructing bubbling solutions to its small perturbations.

Citations

• On Fractional GJMS Operators
• Further results on the fractional Yamabe problem: the umbilic case

Cited by

• Classification of finite energy solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents
• A non-compactness result on the fractional Yamabe problem in large dimensions

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