✦ LIBER ✦

Energy and volume of unit vector fields on three-dimensional Riemannian manifolds

✍ Scribed by J.C. González-Dávila; L. Vanhecke

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 171 KB
Volume: 16
Category: Article
ISSN: 0926-2245
DOI: 10.1016/s0926-2245(02)00060-8

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✦ Synopsis

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.

📜 SIMILAR VOLUMES

Lower Bounds for the Energy of Unit Vect

Lower Bounds for the Energy of Unit Vector Fields and Applications: Volume 152, Number 2 (1998), pages 379–403

✍ Etienne Sandier 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 29 KB

A mistake in the proof of Theorem 1 occurred which was pointed out to the author by Tristan RivieÁ re. It is stated there that the constant C depends only on the domain and the H 1Â2 norm of the boundary data. It really should be the H s -norm for some s>1Â2 for the result to be correct. The proble