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The second Yamabe invariant with singularities

Mohammed BenaliliHichem Boughazi — 2012

Annales mathématiques Blaise Pascal

Let ( M , g ) be a compact Riemannian manifold of dimension n 3 .We suppose that g is a metric in the Sobolev space H 2 p ( M , T * M T * M ) with p > n 2 and there exist a point P 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...

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