Bounds for the Morse index of free boundary minimal surfaces
Differential Geometry
2021-12-10 v3
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.
Keywords
Cite
@article{arxiv.1710.10971,
title = {Bounds for the Morse index of free boundary minimal surfaces},
author = {Vanderson Lima},
journal= {arXiv preprint arXiv:1710.10971},
year = {2021}
}
Comments
Final version. Accepted for publication on Asian Journal of Mathematics