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Séminaire Analyse non linéaire et EDP

Horaires : Le mardi 19 novembre 2013, 10h30

Lieu : IHP, salle 201

Conformal invariants from nodal sets

Dmitry Jakobson (McGill)

We study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant?s Nodal Domain Theorem. We also show that on any manifold of dimension n >= 3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n >= 3. This is joint work with Yaiza Canzani, Rod Gover and Raphael Ponge.


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