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✦   LIBER   ✦

Relationship between volume and energy of vector fields

✍ Scribed by Olga Gil-Medrano

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
127 KB
Volume
15
Category
Article
ISSN
0926-2245

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✦ Synopsis

A unified study of energy and volume functionals is presented here by determining the critical points of a functional that extends simultaneously energy and volume and that is defined on the product of the manifold of smooth maps C ∞ (M, N ) times the manifold M of riemannian metrics on M. The restriction of this functional to different submanifolds of the space of vector fields X(M) Γ— M is also considered, and used to study several functionals generalizing volume and energy or total bending of vector fields.

πŸ“œ SIMILAR VOLUMES

Energy and volume of unit vector fields
Energy and volume of unit vector fields on three-dimensional Riemannian manifolds
✍ J.C. GonzΓ‘lez-DΓ‘vila; L. Vanhecke πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 171 KB

We study the stability and instability of harmonic and minimal unit vector fields and the existence of absolute minima for the energy and volume functional on three-dimensional compact manifolds, in particular on compact quotients of unimodular Lie groups.

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