no. 11-12
Mathematical Analysis/Differential Geometry
Spectral properties of Schrödinger operators on compact manifolds: Rigidity, flows, interpolation and spectral estimates
[Propriétés spectrales dʼopérateurs de Schrödinger sur des variétés compactes : Rigidité, flots, interpolation et estimations spectrales]

Présenté par : the Editorial Board

Dolbeault, Jean1 ; Esteban, Maria J.1 ; Laptev, Ari2 ; Loss, Michael3
1 Ceremade (UMR CNRS 7534), Université Paris-Dauphine, place du Maréchal-de-Lattre-de-Tassigny, 75775 Paris cedex 16, France
2 Department of Mathematics, Imperial College London, Huxley Building, 180 Queenʼs Gate, SW7 2AZ, UK
3 School of Mathematics, Skiles Building, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
Comptes Rendus. Mathématique, Tome 351 (2013) no. 11-12, pp. 437-440.

Cette note est consacrée à des estimations spectrales optimales pour des opérateurs de Schrödinger sur des variétés riemaniennes compactes et simplement connexes, sans bord. Ces estimations sont basées sur certaines inégalités dʼinterpolation et sur un résultat récent de rigidité pour des équations elliptiques non linéaires sur ces variétés.

This note is devoted to optimal spectral estimates for Schrödinger operators on compact connected Riemannian manifolds without boundary. These estimates are based on the use of appropriate interpolation inequalities and on some recent rigidity results for nonlinear elliptic equations on those manifolds.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.06.014
Dolbeault, Jean 1 ; Esteban, Maria J. 1 ; Laptev, Ari 2 ; Loss, Michael 3

1 Ceremade (UMR CNRS 7534), Université Paris-Dauphine, place du Maréchal-de-Lattre-de-Tassigny, 75775 Paris cedex 16, France
2 Department of Mathematics, Imperial College London, Huxley Building, 180 Queenʼs Gate, SW7 2AZ, UK
3 School of Mathematics, Skiles Building, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA 
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     title = {Spectral properties of {Schr\"odinger} operators on compact manifolds: {Rigidity,} flows, interpolation and spectral estimates},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {437--440},
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Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael. Spectral properties of Schrödinger operators on compact manifolds: Rigidity, flows, interpolation and spectral estimates. Comptes Rendus. Mathématique, Tome 351 (2013) no. 11-12, pp. 437-440. doi : 10.1016/j.crma.2013.06.014. http://www.numdam.org/articles/10.1016/j.crma.2013.06.014/

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