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The energy functional on the Virasoro–Bott group with the L 2-metric has no local minima

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Abstract

The geodesic equation for the right invariant L 2-metric (which is a weak Riemannian metric) on each Virasoro–Bott group is equivalent to the KdV-equation. We prove that the corresponding energy functional, when restricted to paths with fixed endpoints, has no local minima. In particular, solutions of KdV do not define locally length-minimizing paths.

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  1. Department of Mathematics, Imperial College London, London, SW7 2AZ, UK

    Martins Bruveris

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  1. Martins Bruveris
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Correspondence to Martins Bruveris.

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Bruveris, M. The energy functional on the Virasoro–Bott group with the L 2-metric has no local minima. Ann Glob Anal Geom 43, 385–395 (2013). https://doi.org/10.1007/s10455-012-9350-0

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  • DOI: https://doi.org/10.1007/s10455-012-9350-0

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