The energy functional on the Virasoro-Bott group with the L2-metric has no local minima

Details The energy functional on the Virasoro-Bott group with the L2-metric has no local minima The energy functional on the Virasoro-Bott group with the L2-metric has no local minima

2011-06-21

arxiv.org/abs/1106.4326v2

Mathematics

Differential Geometry

Scientific paper

The geodesic equation for the right invariant L2 -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 don't define locally length-minimizing paths.

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