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arXiv · 1204.1268

Second Eigenvalue of the Yamabe Operator and Applications

Safaa El Sayed
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Abstract

Let $(M, g)$ be a compact Riemannian manifold of dimension $n \geq 3$. In this paper, we give various properties of the eigenvalues of the Yamabe operator $L_g$. In particular, we show how the second eigenvalue of $L_g$ is related to the existence of nodal solutions of the equation $L_g u = \epsilon | u|^{N-2} u$, where $\epsilon = +1, 0,$ or -1.

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Safaa El Sayed. 2012-04-05. Second Eigenvalue of the Yamabe Operator and Applications. https://arxiv.org/abs/1204.1268

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