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arXiv · 1910.02580

Small fiberwise oscillation of the eigenfunctions of collapsing Einstein manifolds

Shaosai Huang·Selin Taskent
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Abstract

By Cheeger-Colding's almost splitting theorem, if a domain in a Ricci flat manifold is pointed-Gromov-Hausdorff close to a lower dimensional Euclidean domain, then there is a harmonic almost splitting map. We show that any eigenfunction of the Laplace operator is almost constant along the fibers of the almost splitting map, in the $L^2$-average sense. This generalizes an estimate of Fukaya in the case of collapsing with bounded diameter and sectional curvature.

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Shaosai Huang, Selin Taskent. 2019-10-07. Small fiberwise oscillation of the eigenfunctions of collapsing Einstein manifolds. https://arxiv.org/abs/1910.02580

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