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Remarks on the Cwikel–Lieb–Rozenblum and Lieb–Thirring Estimates for Schrödinger Operators on Riemannian Manifolds

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Abstract

Let M be a general complete Riemannian manifold and consider a Schrödinger operator −Δ+V on L 2(M). We prove Cwikel–Lieb–Rozenblum as well as Lieb–Thirring type estimates for −Δ+V. These estimates are given in terms of the potential and the heat kernel of the Laplacian on the manifold. Some of our results hold also for Schrödinger operators with complex-valued potentials.

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Authors and Affiliations

  1. Institut de Mathématiques de Bordeaux (IMB), CNRS UMR 5251, Equipe d’Analyse et Géométrie, Université Bordeaux 1, 351 Cours de la Liberation, 33405, Talence, France

    El Maati Ouhabaz

  2. MIP/CEREMATH, 21 Allée de Brienne, 31000, Toulouse, France

    César Poupaud

Authors
  1. El Maati Ouhabaz
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  2. César Poupaud
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Correspondence to El Maati Ouhabaz.

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Ouhabaz, E.M., Poupaud, C. Remarks on the Cwikel–Lieb–Rozenblum and Lieb–Thirring Estimates for Schrödinger Operators on Riemannian Manifolds. Acta Appl Math 110, 1449–1459 (2010). https://doi.org/10.1007/s10440-009-9519-0

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  • DOI: https://doi.org/10.1007/s10440-009-9519-0

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