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Une inégalité du type “Reilly” pour les sous-variétés de l'espace hyperbolique

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Commentarii Mathematici Helvetici

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Bibliographie

  1. Aubin T.,Nonlinear Analysis on manifolds, Monge-Ampère equation, Grundlehren Math. Wiss., Vol. 252 (1982).

  2. Barbosa L., Do Carmo M.,Stability of hypersurfaces with constant mean curvature, Math. Z.,185, 339–353 (1984).

    Article  MathSciNet  Google Scholar 

  3. Barbosa L., Do Carmo M., Eschenburg J.,Stability of hypersurfaces of constant mean curvature in riemannian manifolds, Math. Z.197, 123–138 (1988).

    Article  MathSciNet  Google Scholar 

  4. Chen B. Y.,Total Mean Curvature and Submanifolds of Finite Type. Series in Pure Math. Vol. 1, World Scientific (1984).

  5. El Soufi A., Ilias S.,Sur l'existence des hypersurfaces minimales stables ou d'indice 1, et des hypersurfaces à courbure moyenne constante stables. Prépublication de l'Institut Fourier (Grenoble), no94, (1987).

  6. El Soufi A., Ilias S.,Immersions minimales, première valeur propre du Laplacien et volume conforme, Math. Ann. 275, 257–267 (1986).

    Article  MathSciNet  Google Scholar 

  7. El Soufi A., Ilias S.,Opérateurs de Schödinger sur une variété riemannienne et volume conforme, Prépublication de l'Institut Fourier (Grenoble), no 83, (1987).

  8. Heintze E., Extrinsic upper bound for λ1, Math. Ann.280, 389–402 (1988).

    Article  MathSciNet  Google Scholar 

  9. Langer J., Singer T. A.,The total squared curvature of closed curves, J. Diff. Geo.20, 1–22 (1984).

    MathSciNet  Google Scholar 

  10. Lawson H. B.,Lectures on minimal submanifolds, Lecture series 9, Berkeley: Publish or perish (1980).

    MATH  Google Scholar 

  11. Li P., Yau S. T.,A new conformal invariant and its application etc, Invent. Math.69, 269–291 (1982).

    Article  MathSciNet  Google Scholar 

  12. Montiel S., Ros A.,Minimal immersions of surfaces by the first eigen functions and conformal area, Invent. Math.83, 153–166 (1986);

    Article  MathSciNet  Google Scholar 

  13. Reilly R. C.,On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space, Comment. Math. Helv.52, 525–533 (1977).

    MathSciNet  Google Scholar 

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El Soufi, A., Ilias, S. Une inégalité du type “Reilly” pour les sous-variétés de l'espace hyperbolique. Commentarii Mathematici Helvetici 67, 167–181 (1992). https://doi.org/10.1007/BF02566494

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  • DOI: https://doi.org/10.1007/BF02566494

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