Conformal metric sequences with integral-bounded scalar curvature

2017/06/13 by Yuxiang Li, Li, Yuxiang, Zhipeng Zhou +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1706.03919

arxiv created 2017/06/29 · arxiv updated 2017/06/30

Abstract

Let (M; g) be a smooth compact Riemiannian manifold without boundary and g_k be a metric conformal to g. Suppose vol(M; g_k)+||R_k||_L^p(M;g_k) < C, where R_k is the scalar curvature and p > (n)/(2). We will use the 3-circle theorem and the John-Nirenberg inequality to study the bubble tree convergence of g_k.

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