BUBBLING ABOVE THE THRESHOLD OF THE SCALAR CURVATURE IN DIMENSIONS FOUR AND FIVE

Abstract : On any closed manifold (M n , g) of dimension n ∈ {4, 5} we exhibit new blow-up configurations for perturbations of a purely critical stationary Schrödinger equation. We construct positive solutions which blow-up as the sum of two isolated bubbles, one of which concentrates at a point ξ where the potential k of the equation satisfies k(ξ) > n − 2 4(n − 1) Sg(ξ), where Sg is the scalar curvature of (M n , g). The latter condition requires the bubbles to blow-up at different speeds and forces us to work at an elevated precision. We take care of this by performing a construction which combines a priori asymptotic analysis methods with a Lyapounov-Schmidt reduction.
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https://hal.archives-ouvertes.fr/hal-01805092
Contributeur : Bruno Premoselli <>
Soumis le : vendredi 1 juin 2018 - 14:05:07
Dernière modification le : mercredi 12 décembre 2018 - 15:17:20
Document(s) archivé(s) le : dimanche 2 septembre 2018 - 15:07:53

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  • HAL Id : hal-01805092, version 1

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Bruno Premoselli, Pierre-Damien Thizy. BUBBLING ABOVE THE THRESHOLD OF THE SCALAR CURVATURE IN DIMENSIONS FOUR AND FIVE. 2018. 〈hal-01805092〉

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