English

Conformal metric sequences with integral-bounded scalar curvature

Differential Geometry 2017-06-30 v3

Abstract

Let (M;g)(M; g) be a smooth compact Riemiannian manifold without boundary and gkg_{k} be a metric conformal to gg. Suppose vol(M;gk)+RkLp(M;gk)<Cvol(M; g_{k})+||R_{k}||_{L^{p}(M;g_{k})} < C, where RkR_{k} is the scalar curvature and p>n2p > \frac{n}{2}. We will use the 3-circle theorem and the John-Nirenberg inequality to study the bubble tree convergence of gkg_{k}.

Keywords

Cite

@article{arxiv.1706.03919,
  title  = {Conformal metric sequences with integral-bounded scalar curvature},
  author = {Yuxiang Li and Zhipeng Zhou},
  journal= {arXiv preprint arXiv:1706.03919},
  year   = {2017}
}