Conformal metric sequences with integral-bounded scalar curvature

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 $p>\frac{n}{2}$. We will use the 3-circle theorem and the John-Nirenberg inequality to study the bubble tree convergence of $g_k$.

Cited by in corpus (3)

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