A link at infinity for minimal surfaces in $\mathbb{R}^4$
Résumé
We look at complete minimal surfaces of finite total curvature in $\mathbb{R}^4$. Similarly to the case of complex curves in $\mathbb{C}^2$ we introduce their link at infinity; we derive the writhe number at infinity which gives a formula for the total normal curvature of the surface. The knowledge of the link at infinity can sometimes help us determine if a surface has self-intersection and we illustrate this idea by looking at genus zero surfaces of small total curvature.
Domaines
Géométrie différentielle [math.DG]Origine | Fichiers produits par l'(les) auteur(s) |
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