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Constant mean curvature spheres in Riemannian manifolds

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Abstract

We prove the existence of embedded spheres with large constant mean curvature in any compact Riemannian manifold (M, g). This result partially generalizes a result of R. Ye which handles the case where the scalar curvature function of the ambient manifold (M, g) has non-degenerate critical points.

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Authors and Affiliations

  1. Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris 12, Creteil Cedex, France

    F. Pacard

  2. Institut Universitaire de France, Paris, France

    F. Pacard

  3. Department of Mathematics, National University of Singapore, 2 Science drive 2, 117543, Singapore, Singapore

    X. Xu

Authors
  1. F. Pacard
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  2. X. Xu
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Correspondence to F. Pacard.

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Pacard, F., Xu, X. Constant mean curvature spheres in Riemannian manifolds. manuscripta math. 128, 275–295 (2009). https://doi.org/10.1007/s00229-008-0230-7

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  • DOI: https://doi.org/10.1007/s00229-008-0230-7

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