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Scalar and mean curvature comparison via \(\mu \)-bubbles

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Abstract

Following ideas of Gromov we prove scalar and mean curvature comparison results for Riemannian bands with lower scalar curvature bounds in dimension \(n\le 7\). The model spaces we use are warped products over scalar-flat manifolds with \(\log \)-concave warping functions.

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Acknowledgements

This work is part of my doctoral dissertation project at Augsburg University. I am grateful to my advisor Bernhard Hanke for his continued support, Johannes Ebert for his expertise regarding Proposition 6.4 and Jan Metzger for answering my questions concerning maximum principles. I thank Rudolf Zeidler, Simone Cecchini and Georg Frenck for helpful comments. This work was supported by a doctoral grant from the German Academic Scholarship Foundation.

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The author was supported by a doctoral grant from the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes).

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  1. Institut für Mathematik, Universität Augsburg, 86135, Augsburg, Germany

    Daniel Räde

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Communicated by Richard M. Schoen.

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Räde, D. Scalar and mean curvature comparison via \(\mu \)-bubbles. Calc. Var. 62, 187 (2023). https://doi.org/10.1007/s00526-023-02520-8

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