The Infimum of the Energy of Unit Vector Fields on Odd-Dimensional Spheres期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

The Infimum of the Energy of Unit Vector Fields on Odd-Dimensional Spheres

Authors:

Vincent Borrelli Fabiano Brito Olga Gil-Medrano

Institution:

(1) Institut Girard Desargues, Université Claude Bernard, Lyon 1, 43, boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France;(2) Departamento de Matemática, IME-USP, Caixa Postal 66281, CEP 05315-970, São Paulo, SP, Brazil;(3) Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Valencia, 46100 Burjassot, Valencia, Spain

Abstract:

We construct a one-parameter family of unit smooth vector fieldsglobally defined on the sphere $\mathbb{S}$ ^2k+1 for k

2, with energyconverging to the energy of the unit radial vector field, which isdefined on the complementary of two antipodal points. So we prove thatthe infimum of the energy of globally defined unit smooth vector fieldsis

$\left( {\frac{{2k + 1}}{2} + \frac{k}{{2k - 1}}} \right){\text{ vol (}}\mathbb{S}^{2k + 1} ).$

Keywords:

energy of vector fields radial fields on spheres minimizing sequence

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏