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

Autor:	Bruveris, Martins
Rok vydání:	2011
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs 35Q53 35A15 58B20 58D05 58D15 58E12
Zdroj:	Ann. Glob. Anal. Geom., 41(4), 461-472, 2012
Druh dokumentu:	Working Paper
DOI:	10.1007/s10455-012-9350-0
Popis:	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 don't define locally length-minimizing paths. Comment: 12 pages, revised version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1106.4326 Zobrazit plný text záznamu View this record from Arxiv