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arXiv · 1504.02066

Minimal hyperspheres of arbitrarily large Morse index

Alessandro Carlotto
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Abstract

We show that the Morse index of a closed minimal hypersurface in a four-dimensional Riemannian manifold cannot be bound in terms of the volume and the topological invariants of the hypersurface itself by presenting a method for constructing Riemannian metrics on S^4 that admit embedded minimal hyperspheres of uniformly bounded volume and arbitrarily large Morse index. The phenomena we exhibit are in striking contrast with the three-dimensional compactness results by Choi-Schoen.

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Alessandro Carlotto. 2015-04-08. Minimal hyperspheres of arbitrarily large Morse index. https://arxiv.org/abs/1504.02066

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