A topological lower bound for the energy of a unit vector field on a closed hypersurface of the euclidean space. The 3-dimensional case

Fabiano G. B. Brito; Andre O. Gomes; Adriana V. Nicoli

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arXiv · 1609.04900

A topological lower bound for the energy of a unit vector field on a closed hypersurface of the euclidean space. The 3-dimensional case

Fabiano G. B. Brito·Andre O. Gomes·Adriana V. Nicoli

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Abstract

In this short note we prove that the degree of the Gauss map {\nu} of a closed 3-dimensional hypersurface of the Euclidean space is a lower bound for the total bending functional B, introduced by G. Wiegmink. Consequently, the energy functional E introduced by C. M. Wood admits a topological lower bound.

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Fabiano G. B. Brito, Andre O. Gomes, Adriana V. Nicoli. 2016-09-16. A topological lower bound for the energy of a unit vector field on a closed hypersurface of the euclidean space. The 3-dimensional case. https://arxiv.org/abs/1609.04900

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