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

被引：2

作者：

Bruveris, Martins ^{[1
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2013年 / 43卷 / 04期

关键词：

Diffeomorphism group; Virasoro group; Geodesic distance; KDV EQUATION; DIFFEOMORPHISMS;

D O I：

10.1007/s10455-012-9350-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：385 / 395

页数：11

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