On perturbations of the fractional Yamabe problem

Woocheol Choi; Seunghyeok Kim

On perturbations of the fractional Yamabe problem

Analysis of PDEs 2015-02-09 v2 Differential Geometry

Authors: Woocheol Choi , Seunghyeok Kim

Abstract

The fractional Yamabe problem, proposed by Gonz\'{a}lez-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.

Keywords

fractional Yamabe problem conformal invariance nonlocal operator bubbling solution perturbation non-compactness scalar curvature

Cite

@article{arxiv.1501.00641,
  title  = {On perturbations of the fractional Yamabe problem},
  author = {Woocheol Choi and Seunghyeok Kim},
  journal= {arXiv preprint arXiv:1501.00641},
  year   = {2015}
}