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arXiv · 1710.10971

Bounds for the Morse index of free boundary minimal surfaces

Vanderson Lima
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Abstract

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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Vanderson Lima. 2017-10-30. Bounds for the Morse index of free boundary minimal surfaces. https://arxiv.org/abs/1710.10971

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