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Journal Articles Mathematische Zeitschrift Year : 2022

On the size of stable minimal surfaces in $${\mathbb {R}}^4$$

Abstract

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 .
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Dates and versions

hal-03864903 , version 1 (22-11-2022)

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Ari Aiolfi, Marc Soret, Marina Ville. On the size of stable minimal surfaces in $${\mathbb {R}}^4$$. Mathematische Zeitschrift, 2022, 302 (2), pp.1155-1170. ⟨10.1007/s00209-022-03097-2⟩. ⟨hal-03864903⟩
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