Closed oriented genus-g surfaces in S^3 have Gauss map area at least 4π(1+g); equality holds only for round spheres, and minimizing embedded sequences bubble into one positive and g negative spherical cycles.
Variational problems for Lagrangian and Legendrian subman ifolds
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Minimizing the Gauss map area of surfaces in $\mathbb{S}^3$
Closed oriented genus-g surfaces in S^3 have Gauss map area at least 4π(1+g); equality holds only for round spheres, and minimizing embedded sequences bubble into one positive and g negative spherical cycles.