Collapsing constant scalar curvature metrics

Jeff Viaclovsky; Xiaokang Wang

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arXiv · 2606.13913

Collapsing constant scalar curvature metrics

Jeff Viaclovsky·Xiaokang Wang

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Abstract

We prove that a sequence of constant scalar curvature (CSC) metrics which is collapsing with bounded curvature to a manifold $(X,g_{\infty})$ can be perturbed to a sequence of $\mathcal{N}$-invariant collapsing CSC metrics, under a natural assumption involving the eigenvalues of the drift Laplacian on $(X,g_{\infty})$. This answers a special case of a question of Cheeger-Fukaya-Gromov. We also give some natural conditions on the limiting metric-measure space under which the eigenvalue assumption is automatically satisfied.

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Jeff Viaclovsky, Xiaokang Wang. 2026-06-11. Collapsing constant scalar curvature metrics. https://arxiv.org/abs/2606.13913

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