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arXiv · 1708.01575

Poincaré index and the volume functional of unit vector fields on punctured spheres

Fabiano G. B. Brito·André O. Gomes·Icaro Gonçalves
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Abstract

For $n\geq 1$, we exhibit a lower bound for the volume of a unit vector field on $\mathbb{S}^{2n+1}\backslash\{\pm p\}$ depending on the absolute values of its Poincaré indices around $\pm p$. We determine which vector fields achieve this volume, and discuss the idea of having multiple isolated singularities of arbitrary configurations.

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Fabiano G. B. Brito, André O. Gomes, Icaro Gonçalves. 2017-09-19. Poincaré index and the volume functional of unit vector fields on punctured spheres. https://arxiv.org/abs/1708.01575

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