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

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

The geodesic equation for the right invariant L super(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, sol...

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Veröffentlicht in:Annals of global analysis and geometry 2013-04, Vol.43 (4), p.385-395
1. Verfasser: Bruveris, Martins
Format: Artikel
Sprache:eng
Schlagworte:
Equivalence
Invariants
Mathematical analysis
Minima
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Zusammenfassung:The geodesic equation for the right invariant L super(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.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-012-9350-0