The second Yamabe invariant with singularities

Benalili, Mohammed; Boughazi, Hichem

Annales mathématiques Blaise Pascal, Tome 19 (2012), p. 147-176 / Harvested from Numdam

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Résumé

Let $(M, g)$ be a compact Riemannian manifold of dimension $n \geq 3$ .We suppose that $g$ is a metric in the Sobolev space $H_{2}^{p} (M, T^{*} M \otimes T^{*} M)$ with $p > \frac{n}{2}$ and there exist a point $P \in M$ and $δ > 0$ such that $g$ is smooth in the ball $B_{p} (δ)$ . We define the second Yamabe invariant with singularities as the infimum of the second eigenvalue of the singular Yamabe operator over a generalized class of conformal metrics to $g$ and of volume $1$ . We show that this operator is attained by a generalized metric, we deduce nodal solutions to a Yamabe type equation with singularities.

Publié le : 2012-01-01

MR 2978317 | Zbl 1256.58005

DOI : https://doi.org/10.5802/ambp.308
Classification: 58J05

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     author = {Benalili, Mohammed and Boughazi, Hichem},
     title = {The second Yamabe invariant with singularities},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {19},
     year = {2012},
     pages = {147-176},
     doi = {10.5802/ambp.308},
     zbl = {1256.58005},
     mrnumber = {2978317},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_2012__19_1_147_0}
}

Benalili, Mohammed; Boughazi, Hichem. The second Yamabe invariant with singularities. Annales mathématiques Blaise Pascal, Tome 19 (2012) pp. 147-176. doi : 10.5802/ambp.308. http://gdmltest.u-ga.fr/item/AMBP_2012__19_1_147_0/

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