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 $vol(M; g_{k})+||R_{k}||<em>{L^{p}(M;g</em>{k})} &lt; C$, where $R_{k}$ is the scalar curvature and $p &gt; \frac{n}{2}$. We will use the 3-circle theorem and the John-Nirenberg inequality to study the bubble tree convergence of $g_{k}$.