2011/06/30 by Martins Bruveris · 3 citations
Mathematics · #Differential geometry #Energy (signal processing) #Energy functional #Geodesic #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Group (periodic table) #Invariant (physics) #Korteweg–de Vries equation #Maxima and minima #Nonlinear Partial Differential Equations #Riemannian manifold #math.AP #math.DG #msc:35A15 #msc:35Q53 #msc:58B20 #msc:58D05 #msc:58D15 #msc:58E12
paper · pdf · doi:10.1007/s10455-012-9350-0
published in Annals of Global Analysis and Geometry 43(4), 385-395 (Springer Science+Business Media) · 12 pages, revised version
openalex publication_date 2012/08/13 · arxiv created 2015/04/08 · arxiv updated 2015/04/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.