# Vector fields with big and small volume on $\mathbb{S}^2$

@inproceedings{Albuquerque2021VectorFW, title={Vector fields with big and small volume on \$\mathbb\{S\}^2\$}, author={Rui Albuquerque}, year={2021} }

We search for minimal volume vector fields on a given Riemann surface, specialising on the case of M?, this is, the 2-sphere with two antipodal points removed. We discuss the homology theory of the unit sphere tangent bundle (SM?, ∂SM?) in relation with calibrations and a minimal volume equation. We find a family Xm,k, k ∈ N, called the meridian type vector fields, defined globally and with unbounded volume on any given open subset Ω of M?. In other words, we have that ∀Ω, limk vol(Xm,k…

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