Comptes Rendus
no. 11-12
Mathematical Analysis/Differential Geometry
Spectral properties of Schrödinger operators on compact manifolds: Rigidity, flows, interpolation and spectral estimates

Presented by: the Editorial Board

Jean Dolbeault1; Maria J. Esteban1; Ari Laptev2; Michael Loss3
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, Volume 351 (2013) no. 11-12, pp. 437-440.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.06.014

Jean Dolbeault 1; Maria J. Esteban 1; Ari Laptev 2; Michael Loss 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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Jean Dolbeault; Maria J. Esteban; Ari Laptev; Michael Loss. Spectral properties of Schrödinger operators on compact manifolds: Rigidity, flows, interpolation and spectral estimates. Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 437-440. doi : 10.1016/j.crma.2013.06.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.06.014/

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