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arXiv · 1803.07787

First eigenvalues of geometric operators under the Yamabe flow

Pak Tung Ho
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Abstract

Suppose $(M,g_0)$ is a compact Riemannian manifold without boundary of dimension $n\geq 3$. Using the Yamabe flow, we obtain estimate for the first nonzero eigenvalue of the Laplacian of $g_0$ with negative scalar curvature in terms of the Yamabe metric in its conformal class. On the other hand, we prove that the first eigenvalue of some geometric operators on a compact Riemannian manifold is nondecreasing along the unnormalized Yamabe flow under suitable curvature assumption. Similar results are obtained for manifolds with boundary and for CR manifold.

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Pak Tung Ho. 2018-03-21. First eigenvalues of geometric operators under the Yamabe flow. https://arxiv.org/abs/1803.07787

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