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Bounds for the Morse index of free boundary minimal surfaces

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arxiv 1710.10971 v3 pith:OLJ2UBMK submitted 2017-10-30 math.DG

Vanderson Lima This is my paper · ORCID
classification math.DG
keywords indexareaminimalboundarysurfaceaboveboundsfree-boundary
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Inspired by work of Ejiri-Micallef on closed minimal surfaces, we compare the energy index and the area index of a free-boundary minimal surface of a Riemannian manifold with boundary, and show that the area index is controlled from above by the area and the topology of the surface. Combining these results with work of Fraser-Li, we conclude that the area index of a free-boundary minimal surface in a convex domain of Euclidean three-space, is bounded from above by a linear function of its genus and its number of boundary components. We also prove index bounds for submanifolds of higher dimension.

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  1. Inequivalent complexity criteria for free boundary minimal surfaces

    math.DG 2019-08 accept novelty 7.0 of 10

    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...

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