Conformal metric sequences with integral-bounded scalar curvature

Abstract

Let (Mg) be a smooth compact Riemiannian manifold without boundary and \(g_k\) be a metric conformal to g. Suppose \(\text{ vol }(M,g_k)+\Vert R_k\Vert _{L^p(M,g_k)}<C\), where \(R_k\) is the scalar curvature and \(p>\frac{n}{2}\). We will use the 3-circles theorem to study the bubble tree convergence of \(g_k\).

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Acknowledgements

The authors would like to thank Prof. Hao Yin for bringing Three Circles Theorem to our attention. The authors also thank Prof. Chong Song for helpful suggestions during the preparation of this paper.

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Correspondence to Zhipeng Zhou.

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Li, Y., Zhou, Z. Conformal metric sequences with integral-bounded scalar curvature. Math. Z. (2020). https://doi.org/10.1007/s00209-020-02533-5

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