In this talk, I will present the metric measure foliation, which is a generalization of Riemannian submersion to a non-smooth setting, and some results about it. This notion was introduced and studied by Galaz-Garcia, Kell, Mondino, and Sosa at first. One of their results is a non-smooth version of Lott’s theorem, which showed a Riemannian submersion preserves the lower bound of Ricci curvature under some assumptions. I studied the relation between the eigenvalues of Laplacian on the total space and them on the base space.

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