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Geodesic completeness for Sobolev H s-metrics on the diffeomorphism group of the circle

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Abstract

We prove that the weak Riemannian metric induced by the fractional Sobolev norm H s on the diffeomorphism group of the circle is geodesically complete, provided that s > 3/2.

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Authors and Affiliations

  1. Institute for Applied Mathematics, University of Hanover, 30167, Hanover, Germany

    Joachim Escher

  2. CNRS, Centrale Marseille, I2M,UMR 7373, Aix Marseille Université, 13453, Marseille, France

    Boris Kolev

Authors
  1. Joachim Escher
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  2. Boris Kolev
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Correspondence to Joachim Escher.

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Escher, J., Kolev, B. Geodesic completeness for Sobolev H s-metrics on the diffeomorphism group of the circle. J. Evol. Equ. 14, 949–968 (2014). https://doi.org/10.1007/s00028-014-0245-3

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  • DOI: https://doi.org/10.1007/s00028-014-0245-3

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