Second Eigenvalue of the Yamabe Operator and Applications

Details Second Eigenvalue of the Yamabe Operator and Applications Second Eigenvalue of the Yamabe Operator and Applications

2012-04-05

arxiv.org/abs/1204.1268v1

Mathematics

Differential Geometry

Scientific paper

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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