[Propriétés spectrales dʼopérateurs de Schrödinger sur des variétés compactes : Rigidité, flots, interpolation et estimations spectrales]
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.
Accepté le :
Publié le :
Jean Dolbeault 1 ; Maria J. Esteban 1 ; Ari Laptev 2 ; Michael Loss 3
@article{CRMATH_2013__351_11-12_437_0, author = {Jean Dolbeault and Maria J. Esteban and Ari Laptev and Michael Loss}, title = {Spectral properties of {Schr\"odinger} operators on compact manifolds: {Rigidity,} flows, interpolation and spectral estimates}, journal = {Comptes Rendus. Math\'ematique}, pages = {437--440}, publisher = {Elsevier}, volume = {351}, number = {11-12}, year = {2013}, doi = {10.1016/j.crma.2013.06.014}, language = {en}, }
TY - JOUR AU - Jean Dolbeault AU - Maria J. Esteban AU - Ari Laptev AU - Michael Loss TI - Spectral properties of Schrödinger operators on compact manifolds: Rigidity, flows, interpolation and spectral estimates JO - Comptes Rendus. Mathématique PY - 2013 SP - 437 EP - 440 VL - 351 IS - 11-12 PB - Elsevier DO - 10.1016/j.crma.2013.06.014 LA - en ID - CRMATH_2013__351_11-12_437_0 ER -
%0 Journal Article %A Jean Dolbeault %A Maria J. Esteban %A Ari Laptev %A Michael Loss %T Spectral properties of Schrödinger operators on compact manifolds: Rigidity, flows, interpolation and spectral estimates %J Comptes Rendus. Mathématique %D 2013 %P 437-440 %V 351 %N 11-12 %I Elsevier %R 10.1016/j.crma.2013.06.014 %G en %F CRMATH_2013__351_11-12_437_0
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/
[1] Sobolev inequalities and Myersʼs diameter theorem for an abstract Markov generator, Duke Math. J., Volume 85 (1996), pp. 253-270
[2] Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations, Invent. Math., Volume 106 (1991), pp. 489-539
[3] Sharp interpolation inequalities on the sphere: New methods and consequences, Chin. Ann. Math. Ser. B, Volume 34 (2013), pp. 99-112
[4] Spectral estimates on the sphere, Anal. Partial Differ. Equ. (2013) (in press, preprint hal-00770755)
[5] J. Dolbeault, M.J. Esteban, M. Loss, Nonlinear flows and rigidity results on compact manifolds, preprint hal-00784887.
[6] Global and local behavior of positive solutions of nonlinear elliptic equations, Commun. Pure Appl. Math., Volume 34 (1981), pp. 525-598
[7] Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities, Courant Lecture Notes in Mathematics, vol. 5, New York University Courant Institute of Mathematical Sciences, New York, 1999
[8] A class of nonlinear conservative elliptic equations in cylinders, Ann. Sc. Norm. Sup. Pisa Cl. Sci. (4), Volume 26 (1998), pp. 249-283
[9] Un théorème dʼannulation pour deséquations elliptiques non linéaires sur des variétés riemanniennes compactes, C. R. Acad. Sci. Paris, Ser. I, Volume 320 (1995), pp. 1337-1342
- On a class of sharp multiplicative Hardy inequalities, St. Petersburg Mathematical Journal, Volume 32 (2021) no. 3, p. 523 | DOI:10.1090/spmj/1659
- Improved Interpolation Inequalities and Stability, Advanced Nonlinear Studies, Volume 20 (2020) no. 2, p. 277 | DOI:10.1515/ans-2020-2080
- The Lowest Eigenvalue of Schrödinger Operators on Compact Manifolds, Potential Analysis, Volume 50 (2019) no. 4, p. 621 | DOI:10.1007/s11118-018-9698-2
- Interpolation Inequalities and Spectral Estimates for Magnetic Operators, Annales Henri Poincaré, Volume 19 (2018) no. 5, p. 1439 | DOI:10.1007/s00023-018-0663-9
- On the proportionality of Chern and Riemannian scalar curvatures, Geometriae Dedicata, Volume 195 (2018) no. 1, p. 57 | DOI:10.1007/s10711-017-0276-3
- Magnetic rings, Journal of Mathematical Physics, Volume 59 (2018) no. 5 | DOI:10.1063/1.5022121
- Uniqueness and rigidity in nonlinear elliptic equations, interpolation inequalities, and spectral estimates, Annales de la Faculté des sciences de Toulouse : Mathématiques, Volume 26 (2017) no. 4, p. 949 | DOI:10.5802/afst.1557
- Rigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces, Inventiones mathematicae, Volume 206 (2016) no. 2, p. 397 | DOI:10.1007/s00222-016-0656-6
- The Moser-Trudinger-Onofri inequality, Chinese Annals of Mathematics, Series B, Volume 36 (2015) no. 5, p. 777 | DOI:10.1007/s11401-015-0976-7
Cité par 9 documents. Sources : Crossref
Commentaires - Politique