On the size of stable minimal surfaces in $${\mathbb {R}}^4$$
Résumé
The Gauss map g of a surface ⌃ in R 4 takes its values in the Grassmannian of oriented 2-planes of R 4 : G + (2, 4). We give geometric criteria of stability for minimal surfaces in R 4 in terms of g. We show in particular that if the spherical area of the Gauss map |g(⌃)| of a minimal surface is smaller than 2⇡ then the surface is stable by deformations which fix the boundary of the surface. This answers the question of [BDC3] in R 4 .
Domaines
Mathématiques [math]| Origine | Fichiers produits par l'(les) auteur(s) |
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