Closed minimal surfaces in the unit sphere satisfy a positive gap theorem for |A|^2 throughout [5/3, 9/5] with an application to rigidity of closed self-shrinkers.
Bryant,Minimal surfaces of constant curvature inS n, Trans
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On Simon's third gap conjecture for minimal surfaces in spheres
Closed minimal surfaces in the unit sphere satisfy a positive gap theorem for |A|^2 throughout [5/3, 9/5] with an application to rigidity of closed self-shrinkers.