The second Yamabe invariant

Details The second Yamabe invariant The second Yamabe invariant

2005-02-04

arxiv.org/abs/math/0502094v2

J. Funct. Anal. 235 no. 2, 377-412 (2006)

Mathematics

Differential Geometry

Scientific paper

Let $(M,g)$ be a compact Riemannian manifold of dimension $n \geq 3$. We
define the second Yamabe invariant as the infimum of the second eigenvalue of
the Yamabe operator over the metrics conformal to $g$ and of volume 1. We study
when it is attained. As an application, we find nodal solutions of the Yamabe
equation.

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