The second Yamabe invariant

Bernd Ammann; Emmanuel Humbert

The second Yamabe invariant

Differential Geometry 2008-02-25 v2

Authors: Bernd Ammann , Emmanuel Humbert

Abstract

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.

Keywords

yamabe problem

Cite

@article{arxiv.math/0502094,
  title  = {The second Yamabe invariant},
  author = {Bernd Ammann and Emmanuel Humbert},
  journal= {arXiv preprint arXiv:math/0502094},
  year   = {2008}
}

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