Under positive scalar curvature and mean-convex boundary, a Morse index bound bounds area, genus, boundary components, and total curvature of free boundary minimal surfaces, while topology or area bounds alone fail to bound the others.
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Inequivalent complexity criteria for free boundary minimal surfaces
Under positive scalar curvature and mean-convex boundary, a Morse index bound bounds area, genus, boundary components, and total curvature of free boundary minimal surfaces, while topology or area bounds alone fail to bound the others.