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arXiv · 1505.06652

Compactness of the space of minimal hypersurfaces with bounded volume and p-th Jacobi eigenvalue

Lucas Ambrozio·Alessandro Carlotto·Ben Sharp
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Abstract

Given a closed Riemannian manifold of dimenion less than eight, we prove a compactness result for the space of closed, embedded minimal hypersurfaces satisfying a volume bound and a uniform lower bound on the first eigenvalue of the stability operator. When the latter assumption is replaced by a uniform lower bound on the p-th Jacobi eigenvalue for p greater or equal than 2 one gains strong convergence to a smooth limit submanifold away from at most p-1 points.

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Lucas Ambrozio, Alessandro Carlotto, Ben Sharp. 2015-09-23. Compactness of the space of minimal hypersurfaces with bounded volume and p-th Jacobi eigenvalue. https://arxiv.org/abs/1505.06652

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